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The document discusses projectile motion and circular motion. It defines key terms related to projectile motion such as trajectory, angle of projection, horizontal range, time of flight, and velocity of projection. It then derives equations for the trajectory, time of flight, horizontal range, maximum height, and velocity at impact of a projectile. Examples and problems are provided to demonstrate the application of these equations.

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Projectiles

The document discusses projectile motion, including that:
1) A projectile's horizontal and vertical motion are independent, with gravity only affecting vertical motion.
2) The path of a projectile is a combination of its horizontal and vertical components - horizontal motion is constant while vertical motion is affected by gravity.
3) Changing the projection angle affects the projectile's altitude and range, with the maximum range occurring at a 45 degree angle.

Projectile Motion

This document discusses projectile motion. It defines a projectile as any body that is given an initial velocity and then follows a path determined by gravitational acceleration and air resistance. Projectiles move in two dimensions, with horizontal and vertical components to their motion. The horizontal velocity is constant, while the vertical velocity changes due to gravity. Together these components produce a parabolic trajectory. The document provides equations to calculate the maximum height, horizontal range, time of flight, and uses an example of kicking a football to demonstrate solving projectile motion problems.

Projecctile motion by sanjeev

The document describes projectile motion and the key concepts involved. It defines a projectile as a particle thrown obliquely near the earth's surface that moves along a curved path. It discusses the trajectory, components of velocity and acceleration, equations of motion, time of flight, range, maximum height, and velocity of a projectile at any instant. Examples of projectile motion calculations are provided to illustrate how to determine initial velocities, maximum height, range, and the time and distance required for a bomb to hit a target from an airplane.

projectile motion

this is all about projectile motion......first few slides are only for presentation ....if needed u can ignore them.....

1.5 projectile motion

A projectile is an object moving under the influence of gravity with a parabolic path. Its motion can be analyzed by separating the horizontal and vertical components. In the horizontal direction, the velocity is constant, while in the vertical direction there is a constant acceleration due to gravity. Projectile motion is used to model many real-world scenarios like thrown objects, diving, and artillery fire. Solving projectile motion problems involves separating the horizontal and vertical motions and using kinematic equations with the initial velocities and gravitational acceleration.

Chapter 2 Motion in a straight line

Class 11 CBSE course work.
This file contains a pdf of the classwork of chapter 3 from the NCERT textbook.

Projectile motion

The document discusses projectile motion and provides sample problems to illustrate the concepts. It begins by defining projectile motion and describing the forces acting on a projectile. It then presents the kinematic equations for the horizontal and vertical motion of a projectile. Several sample problems are worked out applying these equations to calculate values like minimum launch speed, projectile impact location and time, and velocity at impact.

3 equation of motion

The document discusses three equations of motion:
1) The first equation is v=u + at, which gives the velocity acquired by an object with initial velocity u that experiences a uniform acceleration a over time t.
2) The second equation is s=ut + 1/2at^2, which gives the distance traveled by an object with initial velocity u and uniform acceleration a over time t.
3) The third equation is v=u + 2as, which can be derived by eliminating time t from the first two equations and gives the final velocity of an object that travels a distance s with initial velocity u and uniform acceleration a.

Projectiles

The document discusses projectile motion, including that:
1) A projectile's horizontal and vertical motion are independent, with gravity only affecting vertical motion.
2) The path of a projectile is a combination of its horizontal and vertical components - horizontal motion is constant while vertical motion is affected by gravity.
3) Changing the projection angle affects the projectile's altitude and range, with the maximum range occurring at a 45 degree angle.

Projectile Motion

This document discusses projectile motion. It defines a projectile as any body that is given an initial velocity and then follows a path determined by gravitational acceleration and air resistance. Projectiles move in two dimensions, with horizontal and vertical components to their motion. The horizontal velocity is constant, while the vertical velocity changes due to gravity. Together these components produce a parabolic trajectory. The document provides equations to calculate the maximum height, horizontal range, time of flight, and uses an example of kicking a football to demonstrate solving projectile motion problems.

Projecctile motion by sanjeev

The document describes projectile motion and the key concepts involved. It defines a projectile as a particle thrown obliquely near the earth's surface that moves along a curved path. It discusses the trajectory, components of velocity and acceleration, equations of motion, time of flight, range, maximum height, and velocity of a projectile at any instant. Examples of projectile motion calculations are provided to illustrate how to determine initial velocities, maximum height, range, and the time and distance required for a bomb to hit a target from an airplane.

projectile motion

this is all about projectile motion......first few slides are only for presentation ....if needed u can ignore them.....

1.5 projectile motion

A projectile is an object moving under the influence of gravity with a parabolic path. Its motion can be analyzed by separating the horizontal and vertical components. In the horizontal direction, the velocity is constant, while in the vertical direction there is a constant acceleration due to gravity. Projectile motion is used to model many real-world scenarios like thrown objects, diving, and artillery fire. Solving projectile motion problems involves separating the horizontal and vertical motions and using kinematic equations with the initial velocities and gravitational acceleration.

Chapter 2 Motion in a straight line

Class 11 CBSE course work.
This file contains a pdf of the classwork of chapter 3 from the NCERT textbook.

Projectile motion

The document discusses projectile motion and provides sample problems to illustrate the concepts. It begins by defining projectile motion and describing the forces acting on a projectile. It then presents the kinematic equations for the horizontal and vertical motion of a projectile. Several sample problems are worked out applying these equations to calculate values like minimum launch speed, projectile impact location and time, and velocity at impact.

3 equation of motion

The document discusses three equations of motion:
1) The first equation is v=u + at, which gives the velocity acquired by an object with initial velocity u that experiences a uniform acceleration a over time t.
2) The second equation is s=ut + 1/2at^2, which gives the distance traveled by an object with initial velocity u and uniform acceleration a over time t.
3) The third equation is v=u + 2as, which can be derived by eliminating time t from the first two equations and gives the final velocity of an object that travels a distance s with initial velocity u and uniform acceleration a.

Projectile motion by umakant bhaskar gohatre

Projectile motion by umakant bhaskar gohatreSmt. Indira Gandhi College of Engineering, Navi Mumbai, Mumbai

A projectile is any object projected by some means that continues to move due to its own inertia. Projectiles move in two dimensions with both horizontal and vertical velocity components. The horizontal velocity is constant, while the vertical velocity changes due to gravity. Together the components produce the trajectory path, which is parabolic. For horizontally launched projectiles with no initial vertical velocity, the horizontal velocity remains constant while the vertical acceleration is due to gravity. For vertically launched projectiles, the total velocity must be broken into horizontal and vertical components using trigonometry. The kinematic equations can then be applied to each component to solve for time, displacement, or other variables.Simple Harmonic Motion

This Unit is rely on introduction to Simple Harmonic Motion. the contents was prepared using the Curriculum of NTA level 4 at Mineral Resources Institute- Dodoma.

Physics equations of motion

The document discusses three equations of motion:
1) v=u + at, which gives the final velocity (v) of an object with initial velocity (u) under uniform acceleration (a) over time (t).
2) s=ut + 1/2at^2, which gives the distance (s) traveled by an object with initial velocity (u) and acceleration (a) over time (t).
3) v=u+2as, which can be obtained by eliminating time (t) from the first two equations and gives the final velocity (v) of an object that travels a distance (s) with initial velocity (u) and acceleration (a).

Newton's second law of motion

- Sir Isaac Newton published his three laws of motion in 1687 in his book "Philosophiae Naturalis Principia Mathematica", establishing the laws of motion that describe how objects move.
- Newton's second law states that the acceleration of an object depends on the net force acting on the object and its mass, such that acceleration is directly proportional to net force and inversely proportional to mass.
- The equation for Newton's second law is: Force = mass x acceleration (F=ma), where the SI unit for force is the Newton.

statics

This chapter focuses on objects in static equilibrium, where the net force and net torque on the object are both zero. Solving static equilibrium problems involves drawing free body diagrams showing all external forces acting on the object, then resolving forces into components and setting the sums of forces in each direction equal to zero. Three examples are given of solving static equilibrium problems involving particles under the influence of multiple forces. The problems are solved by resolving forces into horizontal and vertical or parallel and perpendicular components, setting the component force equations equal to zero, and solving the equations to determine the magnitudes of unknown forces. Key steps include drawing diagrams, resolving forces, setting force sums to zero, and solving the resulting equations.

Volume of solid revolution

The document discusses different methods for calculating the volume of a solid of revolution: disk method, washer method, and shell method. It provides examples of applying each method to find the volume generated when an area bounded by curves is revolved around an axis. The disk method calculates volume by summing the volumes of thin circular disks. The washer method accounts for holes by subtracting the inner circular area from the outer. The shell method imagines the solid as nested cylindrical shells and sums their individual volumes.

Unit 6, Lesson 3 - Vectors

Unit 6, Lesson 3 - Vectors
Lesson Outline:
1. Vector Representation
2. Graphical Method
3. Mathematical Method
4. Pythagorean Theorem
5. Component Method

Ch 03b motion in a plane

This document outlines concepts from a physics chapter on motion in a plane, including: adding and subtracting vectors using graphical and component methods; defining velocity and acceleration; and describing projectile motion where the horizontal acceleration is zero and the vertical acceleration is -g. Examples of projectile problems are worked through, applying equations of motion.

College Physics 1st Edition Etkina Solutions Manual

This document contains a chapter from the textbook "College Physics" by Etkina, Gentile, and Van Heuvelen. It includes multiple choice and conceptual questions about kinematics concepts like displacement, velocity, acceleration. It also includes practice problems asking students to draw motion diagrams and choose reference frames. The key concepts covered are scalar and vector quantities, relationships between displacement, velocity and acceleration, and using graphs to represent motion.

Buoyancy & floatation

1) Buoyancy is the upward force exerted by a fluid that opposes the weight of an immersed object. This force is equal to the weight of the fluid displaced by the object and allows objects with lower density than the fluid to float.
2) The key factors that determine if an object will float or sink are the density of the object compared to the fluid density, the weight of fluid displaced versus the object's weight, and the object's shape.
3) Stability of floating objects depends on the location of the meta-center point, which is where the line of buoyancy force meets the axis when tilted. Stable equilibrium requires the meta-center to be above the center of gravity

Equations of motion

Motion can be described using concepts like position, displacement, distance, speed, velocity, and acceleration. Position refers to an object's location relative to a reference point, while displacement is the change in position. Distance is how far an object moves, while speed is the rate of change of distance over time. Velocity includes both speed and direction of motion. Acceleration describes the rate of change of velocity over time. Motion diagrams, graphs, and equations are used to quantitatively analyze and describe one-dimensional motion.

Vertical projectile motion

1. The document discusses vertical projectile motion, where objects move up and down under the influence of gravity.
2. Objects in vertical projectile motion experience a constant downward acceleration of 9.8 m/s^2 due to gravity. The time it takes an object to rise is equal to the time it takes to fall back to the initial height.
3. Equations of motion can be used to solve problems involving vertical projectile motion relating to displacement, velocity, acceleration, and time. Position-time and velocity-time graphs are similar to constant acceleration motion and depend on the initial velocity and position coordinates chosen.

Projectile motion 1

Projectile motion is the motion of an object under the influence of gravity. It can be broken down into two components: horizontal motion and vertical motion. Horizontal motion is unaffected by gravity and follows the regular kinematic equations of straight line motion. Vertical motion is affected by the downward acceleration due to gravity and also follows straight line kinematic equations using the acceleration due to gravity. Understanding projectile motion requires analyzing the horizontal and vertical components separately using the appropriate kinematic equations for each direction.

Kinetics of particle

This document contains a presentation on Newton's second law of motion. The presentation topics include the relation between force, mass and acceleration, applications of Newton's second law, equations of motion, and an introduction to kinetics of particles. The document provides definitions and explanations of key concepts such as force, mass, acceleration, momentum, impulse, and kinetics. It also includes sample problems demonstrating applications of Newton's second law and equations of motion, along with step-by-step solutions. The presentation was made by Danyal Haider and Kamran Shah and covers fundamental principles of classical mechanics.

Motion in A plane

Motion can be described in one, two, or three dimensions. One-dimensional motion occurs along a straight line, two-dimensional motion occurs within a plane, and three-dimensional motion occurs in space. Rectilinear motion is one-dimensional motion along a straight path, such as a train moving along tracks. Motion in a plane is two-dimensional and includes circular motion and projectile motion. Motion in space is three-dimensional and describes the motion of objects like planets orbiting the sun. Key variables used to describe motion include displacement, distance, velocity, acceleration, and time.

Velocity Graphs

This document discusses distance-time graphs, velocity-time graphs, and standard units for physical properties. Distance-time graphs show steep lines for fast speeds, shallow lines for slow speeds, and flat lines for zero speed. Velocity is calculated from the gradient of a distance-time graph. Velocity-time graphs show increasing, decreasing, or constant speed. The area under a velocity-time graph equals the distance travelled. Common units for physical properties like distance, time, speed, and mass are also listed.

Lecture: Kinematics

This document provides an overview of kinematics, the study of motion without considering causes. It defines fundamental kinematic concepts like position, displacement, velocity, acceleration and describes how to analyze motion using equations and graphs. Key topics covered include constant acceleration, free fall near Earth's surface, and graphical analysis of motion. The document is intended to help students understand and study the concepts of kinematics.

Kinematic equations of motion

This document provides an overview of kinematic equations and how to approach solving kinematics problems. It includes:
- A list of common kinematic equations and how they are used depending on whether an object starts from rest, has constant velocity, or constant acceleration.
- Guidance on identifying key variables like displacement, velocity, acceleration and determining the correct signs based on the problem context.
- Worked examples showing how to set up and solve kinematics problems step-by-step using the appropriate equations.
- Tips for dealing with problems that may require using multiple equations or are multi-stage problems where acceleration changes. The key is to solve for available variables and use those solutions to determine missing variables

03 kinematics in one dimension

This document provides an outline of key topics in kinematics in one dimension, including:
1. It defines and distinguishes between distance, displacement, speed, velocity, and acceleration. Distance is a scalar quantity while displacement has both magnitude and direction.
2. It provides examples of calculating average and instantaneous velocity and acceleration using kinematic equations.
3. The document contains conceptual questions and worked examples related to these kinematics concepts.

Chapter no. 7 projectile

This document discusses projectile motion and circular motion. It defines key terms like projectile, trajectory, range, time of flight, velocity of projection. It derives equations for the path of a projectile, time of flight, maximum height, and horizontal range. It considers two cases: when a projectile is projected horizontally from a height, and when projected at an angle from a height. Several example problems are provided to demonstrate applying the equations.

Dissertation report

This document presents the layout and introduction for a dissertation report on analyzing multi-storey partially braced frames subjected to seismic and gravity loads using V-braces. The layout includes sections on introduction, literature review, structural analysis methods, earthquake analysis methods, theoretical formulation, results and discussion, conclusion, and references. The introduction discusses the importance of tall structures and braced frames, noting advantages of braced frames include increased strength, stiffness, and reduced member sizes.

ABC Of Project Management

This document provides an overview of project management. It discusses that projects are needed to generate profits for businesses, as profits come from operations which give birth to projects. However, only 34% of projects succeed currently. The document then outlines the basic project life cycle of initiation, planning, execution, controlling, and closing phases. It provides some ABCs of project management, emphasizing always properly defining the project, ensuring stakeholder identification, being aware of constraints and knowledge areas, and cultivating good project management habits and processes within an organization to improve success rates. The overall message is that projects can only succeed by being properly managed to meet defined objectives and baselines.

Projectile motion by umakant bhaskar gohatre

Projectile motion by umakant bhaskar gohatreSmt. Indira Gandhi College of Engineering, Navi Mumbai, Mumbai

A projectile is any object projected by some means that continues to move due to its own inertia. Projectiles move in two dimensions with both horizontal and vertical velocity components. The horizontal velocity is constant, while the vertical velocity changes due to gravity. Together the components produce the trajectory path, which is parabolic. For horizontally launched projectiles with no initial vertical velocity, the horizontal velocity remains constant while the vertical acceleration is due to gravity. For vertically launched projectiles, the total velocity must be broken into horizontal and vertical components using trigonometry. The kinematic equations can then be applied to each component to solve for time, displacement, or other variables.Simple Harmonic Motion

This Unit is rely on introduction to Simple Harmonic Motion. the contents was prepared using the Curriculum of NTA level 4 at Mineral Resources Institute- Dodoma.

Physics equations of motion

The document discusses three equations of motion:
1) v=u + at, which gives the final velocity (v) of an object with initial velocity (u) under uniform acceleration (a) over time (t).
2) s=ut + 1/2at^2, which gives the distance (s) traveled by an object with initial velocity (u) and acceleration (a) over time (t).
3) v=u+2as, which can be obtained by eliminating time (t) from the first two equations and gives the final velocity (v) of an object that travels a distance (s) with initial velocity (u) and acceleration (a).

Newton's second law of motion

- Sir Isaac Newton published his three laws of motion in 1687 in his book "Philosophiae Naturalis Principia Mathematica", establishing the laws of motion that describe how objects move.
- Newton's second law states that the acceleration of an object depends on the net force acting on the object and its mass, such that acceleration is directly proportional to net force and inversely proportional to mass.
- The equation for Newton's second law is: Force = mass x acceleration (F=ma), where the SI unit for force is the Newton.

statics

This chapter focuses on objects in static equilibrium, where the net force and net torque on the object are both zero. Solving static equilibrium problems involves drawing free body diagrams showing all external forces acting on the object, then resolving forces into components and setting the sums of forces in each direction equal to zero. Three examples are given of solving static equilibrium problems involving particles under the influence of multiple forces. The problems are solved by resolving forces into horizontal and vertical or parallel and perpendicular components, setting the component force equations equal to zero, and solving the equations to determine the magnitudes of unknown forces. Key steps include drawing diagrams, resolving forces, setting force sums to zero, and solving the resulting equations.

Volume of solid revolution

The document discusses different methods for calculating the volume of a solid of revolution: disk method, washer method, and shell method. It provides examples of applying each method to find the volume generated when an area bounded by curves is revolved around an axis. The disk method calculates volume by summing the volumes of thin circular disks. The washer method accounts for holes by subtracting the inner circular area from the outer. The shell method imagines the solid as nested cylindrical shells and sums their individual volumes.

Unit 6, Lesson 3 - Vectors

Unit 6, Lesson 3 - Vectors
Lesson Outline:
1. Vector Representation
2. Graphical Method
3. Mathematical Method
4. Pythagorean Theorem
5. Component Method

Ch 03b motion in a plane

This document outlines concepts from a physics chapter on motion in a plane, including: adding and subtracting vectors using graphical and component methods; defining velocity and acceleration; and describing projectile motion where the horizontal acceleration is zero and the vertical acceleration is -g. Examples of projectile problems are worked through, applying equations of motion.

College Physics 1st Edition Etkina Solutions Manual

This document contains a chapter from the textbook "College Physics" by Etkina, Gentile, and Van Heuvelen. It includes multiple choice and conceptual questions about kinematics concepts like displacement, velocity, acceleration. It also includes practice problems asking students to draw motion diagrams and choose reference frames. The key concepts covered are scalar and vector quantities, relationships between displacement, velocity and acceleration, and using graphs to represent motion.

Buoyancy & floatation

1) Buoyancy is the upward force exerted by a fluid that opposes the weight of an immersed object. This force is equal to the weight of the fluid displaced by the object and allows objects with lower density than the fluid to float.
2) The key factors that determine if an object will float or sink are the density of the object compared to the fluid density, the weight of fluid displaced versus the object's weight, and the object's shape.
3) Stability of floating objects depends on the location of the meta-center point, which is where the line of buoyancy force meets the axis when tilted. Stable equilibrium requires the meta-center to be above the center of gravity

Equations of motion

Motion can be described using concepts like position, displacement, distance, speed, velocity, and acceleration. Position refers to an object's location relative to a reference point, while displacement is the change in position. Distance is how far an object moves, while speed is the rate of change of distance over time. Velocity includes both speed and direction of motion. Acceleration describes the rate of change of velocity over time. Motion diagrams, graphs, and equations are used to quantitatively analyze and describe one-dimensional motion.

Vertical projectile motion

1. The document discusses vertical projectile motion, where objects move up and down under the influence of gravity.
2. Objects in vertical projectile motion experience a constant downward acceleration of 9.8 m/s^2 due to gravity. The time it takes an object to rise is equal to the time it takes to fall back to the initial height.
3. Equations of motion can be used to solve problems involving vertical projectile motion relating to displacement, velocity, acceleration, and time. Position-time and velocity-time graphs are similar to constant acceleration motion and depend on the initial velocity and position coordinates chosen.

Projectile motion 1

Projectile motion is the motion of an object under the influence of gravity. It can be broken down into two components: horizontal motion and vertical motion. Horizontal motion is unaffected by gravity and follows the regular kinematic equations of straight line motion. Vertical motion is affected by the downward acceleration due to gravity and also follows straight line kinematic equations using the acceleration due to gravity. Understanding projectile motion requires analyzing the horizontal and vertical components separately using the appropriate kinematic equations for each direction.

Kinetics of particle

This document contains a presentation on Newton's second law of motion. The presentation topics include the relation between force, mass and acceleration, applications of Newton's second law, equations of motion, and an introduction to kinetics of particles. The document provides definitions and explanations of key concepts such as force, mass, acceleration, momentum, impulse, and kinetics. It also includes sample problems demonstrating applications of Newton's second law and equations of motion, along with step-by-step solutions. The presentation was made by Danyal Haider and Kamran Shah and covers fundamental principles of classical mechanics.

Motion in A plane

Motion can be described in one, two, or three dimensions. One-dimensional motion occurs along a straight line, two-dimensional motion occurs within a plane, and three-dimensional motion occurs in space. Rectilinear motion is one-dimensional motion along a straight path, such as a train moving along tracks. Motion in a plane is two-dimensional and includes circular motion and projectile motion. Motion in space is three-dimensional and describes the motion of objects like planets orbiting the sun. Key variables used to describe motion include displacement, distance, velocity, acceleration, and time.

Velocity Graphs

This document discusses distance-time graphs, velocity-time graphs, and standard units for physical properties. Distance-time graphs show steep lines for fast speeds, shallow lines for slow speeds, and flat lines for zero speed. Velocity is calculated from the gradient of a distance-time graph. Velocity-time graphs show increasing, decreasing, or constant speed. The area under a velocity-time graph equals the distance travelled. Common units for physical properties like distance, time, speed, and mass are also listed.

Lecture: Kinematics

This document provides an overview of kinematics, the study of motion without considering causes. It defines fundamental kinematic concepts like position, displacement, velocity, acceleration and describes how to analyze motion using equations and graphs. Key topics covered include constant acceleration, free fall near Earth's surface, and graphical analysis of motion. The document is intended to help students understand and study the concepts of kinematics.

Kinematic equations of motion

This document provides an overview of kinematic equations and how to approach solving kinematics problems. It includes:
- A list of common kinematic equations and how they are used depending on whether an object starts from rest, has constant velocity, or constant acceleration.
- Guidance on identifying key variables like displacement, velocity, acceleration and determining the correct signs based on the problem context.
- Worked examples showing how to set up and solve kinematics problems step-by-step using the appropriate equations.
- Tips for dealing with problems that may require using multiple equations or are multi-stage problems where acceleration changes. The key is to solve for available variables and use those solutions to determine missing variables

03 kinematics in one dimension

This document provides an outline of key topics in kinematics in one dimension, including:
1. It defines and distinguishes between distance, displacement, speed, velocity, and acceleration. Distance is a scalar quantity while displacement has both magnitude and direction.
2. It provides examples of calculating average and instantaneous velocity and acceleration using kinematic equations.
3. The document contains conceptual questions and worked examples related to these kinematics concepts.

Chapter no. 7 projectile

This document discusses projectile motion and circular motion. It defines key terms like projectile, trajectory, range, time of flight, velocity of projection. It derives equations for the path of a projectile, time of flight, maximum height, and horizontal range. It considers two cases: when a projectile is projected horizontally from a height, and when projected at an angle from a height. Several example problems are provided to demonstrate applying the equations.

Projectile motion by umakant bhaskar gohatre

Projectile motion by umakant bhaskar gohatre

Simple Harmonic Motion

Simple Harmonic Motion

Physics equations of motion

Physics equations of motion

Newton's second law of motion

Newton's second law of motion

statics

statics

Volume of solid revolution

Volume of solid revolution

Unit 6, Lesson 3 - Vectors

Unit 6, Lesson 3 - Vectors

Ch 03b motion in a plane

Ch 03b motion in a plane

College Physics 1st Edition Etkina Solutions Manual

College Physics 1st Edition Etkina Solutions Manual

Buoyancy & floatation

Buoyancy & floatation

Equations of motion

Equations of motion

Vertical projectile motion

Vertical projectile motion

Projectile motion 1

Projectile motion 1

Kinetics of particle

Kinetics of particle

Motion in A plane

Motion in A plane

Velocity Graphs

Velocity Graphs

Lecture: Kinematics

Lecture: Kinematics

Kinematic equations of motion

Kinematic equations of motion

03 kinematics in one dimension

03 kinematics in one dimension

Chapter no. 7 projectile

Chapter no. 7 projectile

Dissertation report

This document presents the layout and introduction for a dissertation report on analyzing multi-storey partially braced frames subjected to seismic and gravity loads using V-braces. The layout includes sections on introduction, literature review, structural analysis methods, earthquake analysis methods, theoretical formulation, results and discussion, conclusion, and references. The introduction discusses the importance of tall structures and braced frames, noting advantages of braced frames include increased strength, stiffness, and reduced member sizes.

ABC Of Project Management

This document provides an overview of project management. It discusses that projects are needed to generate profits for businesses, as profits come from operations which give birth to projects. However, only 34% of projects succeed currently. The document then outlines the basic project life cycle of initiation, planning, execution, controlling, and closing phases. It provides some ABCs of project management, emphasizing always properly defining the project, ensuring stakeholder identification, being aware of constraints and knowledge areas, and cultivating good project management habits and processes within an organization to improve success rates. The overall message is that projects can only succeed by being properly managed to meet defined objectives and baselines.

Equilibrium

This document discusses the topic of equilibrium of rigid bodies. It covers:
- Analytical and graphical conditions for equilibrium of co-planar forces.
- Different types of beam supports like simple, pinned, roller, and fixed supports.
- Free body diagrams and their application in analyzing equilibrium and determining reactions.
- Lami's theorem which states that for three forces in equilibrium, each force is proportional to the sine of the angle between the other two forces.
- Examples of problems involving cylinders, pulleys, beams, and friction on inclined planes.

Chapter no. 6 linear mo

This document discusses linear motion and its related concepts. It defines kinematics as the study of motion without consideration of forces, and kinetics as the study of motion with consideration of forces. It then discusses various types of linear motion including rectilinear motion, motion under gravity, and motion under variable acceleration. Key concepts defined include displacement, velocity, acceleration, uniform motion, and graphical representation of motion using displacement-time and velocity-time curves. Equations of motion are provided for rectilinear motion and motion under gravity with uniform acceleration.

Work power energy

1) This document discusses work, power, and energy. It defines work as the product of force and displacement, and defines the units of work as newton-meters (Nm) or joules (J).
2) Power is defined as the rate of doing work, or the ratio of work to time. The units of power are watts (W).
3) Energy exists in various forms including mechanical, thermal, chemical, light, sound, nuclear, and electrical. Mechanical energy includes potential energy, which depends on position or height, and kinetic energy, which depends on motion or velocity.
4) The work-energy principle states that the work done on an object equals its change in

2. linear kinematics i

1. Linear kinematics describes motion using position, velocity, and acceleration without regard to forces. It includes linear (straight line) and curvilinear (bent line) motion.
2. Angular kinematics describes rotational motion like elbow flexion or spinning.
3. General motion combines translation and rotation, describing most human and sports motions.
4. Key descriptors include position, distance/displacement, speed/velocity, and acceleration. Displacement is the straight-line distance between start and end points while distance is the total path length. Velocity describes speed with direction and acceleration is the rate of change of velocity.

Chapter 2 beam

This chapter discusses beams and support reactions. It defines statically determinate beams and describes the following topics: types of beam supports including simple, pin/hinged, roller, and fixed supports; types of beams such as simply supported, cantilever, overhang, and continuous beams; types of loading including concentrated/point loads and distributed loads such as uniform, uniformly varying, and non-uniform loads; and the procedure to find support reactions of statically determinate beams using equilibrium conditions. It also discusses compound beams and the concept of virtual work.

Centre of Gravity

1) The document discusses concepts related to centroid and moment of inertia including: the centroid is the point where the total area of a plane figure is assumed to be concentrated; formulas are provided for finding the centroid of basic shapes; the difference between centroid and center of gravity is explained; properties and methods for finding the centroid are described such as using moments.
2) Formulas are given for moment of inertia including how it is calculated about different axes and the parallel axis theorem.
3) Example problems are provided to demonstrate calculating the centroid and moment of inertia for various shapes.

Water Management

This document provides information about water management topics including sources of water, dams, canals, and irrigation methods. It discusses surface and underground water sources like ponds, lakes, rivers, wells, and tube wells. It describes different types of dams such as earth dams, rock-fill dams, gravity dams, and arch dams. Canals are described as the trenches that distribute water from reservoirs for irrigation. Various irrigation methods are outlined including flow irrigation, flood irrigation, storage irrigation, drip irrigation, and spray irrigation. Rainwater harvesting is introduced as a way to conserve water by collecting and filtering rainwater runoff and roof runoff to recharge underground water sources.

Lahaja za kiswahili kwa ujumla

Lahaja za Kiswahili zimekuwa zikichanganya watumiaji wengi na watu wengi wanaojifunza lugha ya Kiswahili, hivyo matini hii imekusudia kuondoa mkanganyiko huo.

Assignment no 3

This document contains 18 problems related to calculating beam support reactions using concepts like types of beam supports, virtual work, simply supported beams, overhanging beams, cantilever beams, beam bents, and compound beams. The problems include calculating support reactions for various beams under different loading conditions like point loads, uniformly distributed loads, and concentrated moments. Solutions are provided for some of the problems.

D alemberts principle

D'Alembert's Principle states that the resultant of all external forces and inertia forces acting on a body is zero for the body to be in dynamic equilibrium. Inertia forces are represented as minus mass times acceleration. The principle allows equations of static equilibrium to be applied to bodies undergoing translational motion by considering an imaginary inertia force equal and opposite to actual inertia. Several example problems are provided applying the principle to analyze motion of connected bodies over pulleys, motion on inclined planes, and motion within elevators.

Assignment no. 4

This document contains an assignment on analyzing forces in truss structures using the method of joints and method of sections. It provides 10 problems analyzing different truss configurations, requesting the forces in specific members given load and support conditions. The problems include trusses with various spans, loads, and support types, including cantilever trusses.

02 - Structure and Properties of Organic Molecules - Wade 7th

The document summarizes key concepts from Chapter 2 of an organic chemistry textbook, including:
1) Molecular orbital theory and how atomic orbitals combine to form sigma and pi bonds via hybridization. Common hybridizations include sp, sp2, and sp3.
2) Molecular shapes are determined by hybridization and VSEPR theory. Common geometries are linear, trigonal planar, and tetrahedral.
3) Intermolecular forces like hydrogen bonding, dipole-dipole interactions, and London dispersion forces influence physical properties like boiling points and solubility.
4) Isomerism can occur via constitutional isomers with different bonding connectivities or geometric isomers with different spatial arrangements.

01 - Introduction and Review - Wade 7th

This document provides an introduction to organic chemistry, covering topics such as:
- The definition of organic chemistry as the study of carbon compounds.
- Electronic structure of atoms and how they bond through ionic and covalent bonding.
- Resonance structures and how they are used to represent molecules.
- Factors that influence acidity such as electronegativity, size, and resonance.
- The definitions of nucleophiles and electrophiles and their roles in bond formation.

Oganic II - Klein - chapter 22

This document introduces reactions that take place at the alpha carbon of carbonyl compounds. It discusses enols and enolates, which are reactive intermediates that allow substitutions and additions to occur at the alpha carbon. Specifically, it covers alpha halogenation, aldol reactions, and aldol condensations. These reactions are important methods to form carbon-carbon bonds and install functional groups at the alpha position of carbonyls.

07 - Structure and Synthesis of Alkenes - Wade 7th

This chapter discusses alkenes, which are hydrocarbons containing carbon-carbon double bonds. It covers the structure and bonding of ethylene as well as the IUPAC nomenclature used for naming alkenes. The chapter also examines methods for synthesizing alkenes, including dehydrohalogenation reactions and dehydration of alcohols. It discusses substituent effects on the stability of double bonds and various physical properties of alkenes.

STABILITY: Fully & Partially Submerged Bodies

The document discusses the stability of fully and partially submerged bodies. It defines stability as a body's ability to right itself from a heeled position. It describes the center of buoyancy and gravity, and how their relationship determines if a body is in a stable, neutral, or unstable equilibrium. For fully submerged bodies, it states stability occurs when the center of gravity is below the centroid, and instability when it is above. For partially submerged or floating bodies, stability depends on the metacenter and metacenteric height.

Applied mechanics

The document provides an overview of mechanics and engineering mechanics. It discusses key topics including types of mechanics, units of measurement, fundamental concepts like forces and moments. It also summarizes various types of force systems and the laws and methods for analyzing coplanar forces, including the parallelogram law, Varignon's theorem, and analytical and graphical methods for determining the resultant of coplanar concurrent forces.

Dissertation report

Dissertation report

ABC Of Project Management

ABC Of Project Management

Equilibrium

Equilibrium

Chapter no. 6 linear mo

Chapter no. 6 linear mo

Work power energy

Work power energy

2. linear kinematics i

2. linear kinematics i

Chapter 2 beam

Chapter 2 beam

Centre of Gravity

Centre of Gravity

Water Management

Water Management

Lahaja za kiswahili kwa ujumla

Lahaja za kiswahili kwa ujumla

Assignment no 3

Assignment no 3

Mofolojia ya kiswahili

Mofolojia ya kiswahili

D alemberts principle

D alemberts principle

Assignment no. 4

Assignment no. 4

02 - Structure and Properties of Organic Molecules - Wade 7th

02 - Structure and Properties of Organic Molecules - Wade 7th

01 - Introduction and Review - Wade 7th

01 - Introduction and Review - Wade 7th

Oganic II - Klein - chapter 22

Oganic II - Klein - chapter 22

07 - Structure and Synthesis of Alkenes - Wade 7th

07 - Structure and Synthesis of Alkenes - Wade 7th

STABILITY: Fully & Partially Submerged Bodies

STABILITY: Fully & Partially Submerged Bodies

Applied mechanics

Applied mechanics

Projectile

This document provides tips and guidelines for taking online classes. It recommends being prepared before class starts, treating online courses seriously, holding oneself accountable, practicing time management, creating a dedicated study space, eliminating distractions, figuring out how one learns best, and actively participating. During class, it advises opening one's camera, muting audio when not speaking, taking notes by hand rather than on the screen, and only asking or sharing after getting permission. The document also contains information on projectile motion, including definitions, equations of motion, maximum height, time of flight, range, and examples of horizontal and oblique projection.

Projectile motion

A projectile is any object that moves freely through space under the influence of gravity. It follows a parabolic trajectory. Projectile motion is described using equations of linear motion as the projectile moves simultaneously in horizontal and vertical directions. The initial velocity can be resolved into horizontal and vertical components. The maximum height and range of a projectile depend on the initial velocity and angle of projection. Equations are derived to calculate velocities, displacements, flight time, maximum height and range for projectiles projected on horizontal and elevated surfaces. Examples show applications to problems involving projectile motion.

Introduction to linear kinematics

This document provides an introduction to linear kinematics. It discusses key linear kinematic variables like distance, displacement, speed, velocity, and acceleration. It defines these variables and the units used to measure them. It also describes the difference between scalar and vector quantities as they relate to motion. Examples of single-point and multi-segment models for describing motion are provided. Equations for calculating speed, velocity, and acceleration from changes in distance, displacement, and time are shown. Projectile motion is also summarized, including the independent vertical and horizontal components of projectile motion.

Physics 504 Chapter 10 Uniformly Accelerated Rectilinear Motion

This document discusses uniformly accelerated rectilinear motion. It introduces kinematics, which is the study of motion without considering causes, and kinetics, which considers the forces that cause motion. Rectilinear motion refers to motion along a straight line, while curvilinear motion is along a curved path. Formulas are provided for calculating final velocity, distance, and acceleration from gravity for vertical motion. Sample problems demonstrate applying the formulas to problems involving projectile motion.

Presentation on Projectile Motion AIUB Physics

The document discusses projectile motion and how to calculate the distance traveled by a projectile using equations of motion. It provides the equations to calculate horizontal and vertical motion independently as well as the equation for maximum horizontal range. An example problem is included to demonstrate using the equations to find time in air and initial launch speed for an object rolling off a table. The key details are that projectile motion can be analyzed by separating horizontal and vertical components, the maximum range occurs at a launch angle of 45 degrees, and the provided equations can be used to solve problems involving projectiles.

PHY-1-PRESENTATIONbznznznznznxnxbxb.pptx

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Ch 12 (4) Curvilinear Motion X-Y Coordinate.pptx

The document discusses kinematics of particles and projectile motion. It defines projectile motion as any object propelled through space by a force that ceases after launch. Projectile motion involves two-dimensional rectilinear motion with acceleration in the vertical direction due to gravity but no acceleration horizontally. Equations of motion are provided for the horizontal and vertical components. Examples are given of solving projectile motion problems by setting up the appropriate kinematic equations and solving simultaneously for variables like time, velocity, distance, etc.

Projectile-Motion..pptx

The document discusses projectile motion and how to analyze the trajectory of objects in motion under only the force of gravity. It describes projectile motion as motion with constant horizontal velocity and constant vertical acceleration due to gravity. The document provides examples of calculating the maximum height, time of flight, range, and impact velocity of various projectiles using their initial velocity and launch angle. It also relates the initial horizontal and vertical velocity components to the overall initial speed and launch angle.

projectile motion grade 9-170213175803.pptx

This document discusses projectile motion and provides examples to solve related problems. It begins by defining a projectile as any object projected by some means. Projectiles move in two dimensions, with a horizontal velocity component that is constant and a vertical component that changes due to gravity. The types of projectile motion covered are horizontally and vertically launched projectiles. Kinematic equations are provided to solve problems involving projectiles. Examples are worked through, such as calculating the time and distance for a kicked football. Basics of projectile motion are outlined.

PROJECTILE MOTION

1) Projectile motion describes the trajectory of objects thrown or projected into the air. It is the motion of projectiles that are subject only to gravity.
2) Projectiles have two velocity components - a horizontal component that remains constant, and a vertical component that changes due to gravity. This results in a parabolic trajectory.
3) There are two types of projectile motion - horizontally launched, where the initial vertical velocity is zero, and vertically launched, where the velocity has horizontal and vertical components.

18 dynamics applications of derivative -

This document contains 30 problems related to dynamics and applications of derivatives. The problems cover topics like rectilinear motion with variable acceleration, boats moving across rivers, projectile motion, particles moving under constant acceleration, and bodies in vertical motion under gravity. The final problem proves that the ratios of ranges and maximum heights of two projectiles grazing a wall are independent of their initial velocities.

Projectiles

Discusses projectile motion as two dimensional motion.
**More good stuff available at:
www.wsautter.com
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projectile motion horizontal vertical -170213175803 (1).pdf

This document provides information about projectile motion. It defines a projectile as any object projected by some means. Projectiles move in two dimensions, with a horizontal velocity component that is constant and a vertical component that changes due to gravity. The path of a projectile is parabolic. There are two types of projectile motion: horizontally launched, where the initial vertical velocity is zero; and vertically launched, where the velocity must be broken into horizontal and vertical components using trigonometry. Kinematic equations are used to analyze the motion by treating the horizontal and vertical motions separately. Examples are provided to demonstrate solving problems for variables like time, displacement, velocity, and height using the appropriate kinematic equations.

projectile motion horizontal vertical -170213175803 (1).pdf

This document provides information about projectile motion. It defines a projectile as any object projected by some means. Projectiles move in two dimensions, with a horizontal velocity component that is constant and a vertical component that changes due to gravity. The path of a projectile is parabolic. There are two types of projectile motion: horizontally launched, where the initial vertical velocity is zero; and vertically launched, where the velocity must be broken into horizontal and vertical components using trigonometry. Kinematic equations are used to analyze the motion by treating the horizontal and vertical motions separately. Examples are provided to demonstrate solving problems for variables like time, displacement, velocity, and height using the appropriate kinematic equations.

Chapter 3

This document summarizes projectile motion in two dimensions. It explains that a projectile's curved motion can be analyzed as the combination of horizontal and vertical linear motion. In the horizontal direction, the motion is at a constant speed due to the lack of acceleration. In the vertical direction, gravity causes acceleration, resulting in parabolic motion. The document provides an example problem of analyzing the motion of a cannon ball fired at an angle, solving for variables like time, distance, and the equation of its parabolic path. It also gives another example of determining how far a ball will land after rolling off a table.

PROJECTILE MOTION-Horizontal and Vertical

This document provides an overview of projectile motion, including definitions, key concepts, and example problems. It begins by defining a projectile as any object projected by some means that continues to move due to its own inertia. It then explains that projectiles move in two dimensions, with horizontal and vertical velocity components. The horizontal velocity is constant, while the vertical velocity changes due to gravity. Example problems demonstrate using kinematic equations to solve for time, displacement, velocity and height in horizontally and vertically launched projectiles. Key concepts, equations and evaluation problems are provided to reinforce understanding of projectile motion.

Kinematics questions

This document provides information about kinematics topics for competitive exams. It includes an index of topics such as rectilinear motion, projectile motion, and relative motion. Under rectilinear motion, it discusses introduction to rest and motion, frames of reference, distance/displacement, speed and velocity, acceleration, non-uniform acceleration, and graphs related to distance-time, speed-time, and acceleration-time. Projectile motion topics include introduction to projectiles, oblique projectiles, horizontal projectiles, projectiles on a moving platform, projectiles on an inclined plane, and elastic collisions of projectiles. Relative motion discusses introduction, river boat problems, wind airplane problems, rain umbrella problems, velocity of approach/separation, conditions for

Physics 2 LT3: Projectile Motion Solutions

A projectile motion problem is given involving a projectile fired at an angle of 60 degrees with an initial speed of 30 m/s. The initial horizontal and vertical velocities are calculated. The range and time to highest point are also calculated. A second problem involves a shell fired from a cliff and calculations to determine the initial velocity and velocities when it hits the ground. A third problem involves calculating velocities and angle for a kicked football given the range and time.

Projektielbeweging e

1) Gravitational acceleration is the acceleration experienced by objects due to gravity in the absence of other forces like air resistance. On Earth, gravitational acceleration is approximately 9.8 m/s2 directed downward.
2) Formulas are provided for gravitational acceleration based on Newton's law of universal gravitation, as well as kinematic equations of motion involving displacement, velocity, acceleration, and time.
3) Several example problems are worked through applying the kinematic equations to situations like objects being dropped, thrown upwards, or moving upwards/downwards together to calculate values like time, velocity, displacement, and maximum height reached.

Projectile

Projectile

Projectile motion

Projectile motion

Introduction to linear kinematics

Introduction to linear kinematics

Physics 504 Chapter 10 Uniformly Accelerated Rectilinear Motion

Physics 504 Chapter 10 Uniformly Accelerated Rectilinear Motion

Presentation on Projectile Motion AIUB Physics

Presentation on Projectile Motion AIUB Physics

PHY-1-PRESENTATIONbznznznznznxnxbxb.pptx

PHY-1-PRESENTATIONbznznznznznxnxbxb.pptx

chapter 2_Projectile_Motion final (1) (1).pdf

chapter 2_Projectile_Motion final (1) (1).pdf

Ch 12 (4) Curvilinear Motion X-Y Coordinate.pptx

Ch 12 (4) Curvilinear Motion X-Y Coordinate.pptx

Projectile-Motion..pptx

Projectile-Motion..pptx

projectile motion grade 9-170213175803.pptx

projectile motion grade 9-170213175803.pptx

PROJECTILE MOTION

PROJECTILE MOTION

18 dynamics applications of derivative -

18 dynamics applications of derivative -

Projectiles

Projectiles

projectile motion horizontal vertical -170213175803 (1).pdf

projectile motion horizontal vertical -170213175803 (1).pdf

projectile motion horizontal vertical -170213175803 (1).pdf

projectile motion horizontal vertical -170213175803 (1).pdf

Chapter 3

Chapter 3

PROJECTILE MOTION-Horizontal and Vertical

PROJECTILE MOTION-Horizontal and Vertical

Kinematics questions

Kinematics questions

Physics 2 LT3: Projectile Motion Solutions

Physics 2 LT3: Projectile Motion Solutions

Projektielbeweging e

Projektielbeweging e

Transportation engineering

This document provides an overview of transportation engineering and related topics through a presentation. It begins with an introduction to various modes of transportation including roads, bridges, railways, airports, docks and harbors. It then provides a question bank with sample questions on these topics from previous years. The document concludes by providing detailed answers to some of the sample questions, covering areas like classifications of roads and transportation, structures of roads, and short notes on specific road types.

Chapter wise question papers_bce

This document contains a question bank for the Basic Civil Engineering subject divided into 9 units. Each unit contains 6 questions related to topics within that unit. The questions range from 3-10 marks and cover topics such as sub-branches of civil engineering, surveying, remote sensing, dams, roads, building construction principles, materials, and steel structures. This question bank can be used to prepare for exams on basic civil engineering concepts and their applications.

Design of staircase_practical_example

The document provides design details for staircases on three floors of a building, including dimensions, load calculations, and reinforcement details. Load calculations are performed to determine bending moments and shear forces. Reinforcement area, bar diameter, and spacing are calculated for the waist slabs of each staircase to resist the determined bending moment and satisfy code requirements for minimum steel and shear capacity.

Presentation "Use of coupler Splices for Reinforcement"

This document presents a summary of a presentation on the use of coupler splices for reinforcement. The presentation includes an introduction to coupler splices, a literature review on the topic, details on the experimental procedure used to test coupler splices, a cost analysis comparing coupler splices to lap splices, and conclusions. The experimental results show that coupler splices performed better than lap splices and welded splices in tensile loading tests. A cost analysis also determined that coupler splices provide significant cost savings over lap splices by reducing the amount of reinforcement required. The conclusion is that coupler splices are an effective and economic replacement for lap splices in reinforcement.

Guidelines_for_building_design

This document provides guidelines for the design of reinforced concrete structures in buildings according to the limit state method. It outlines the general process for building design which includes studying architectural drawings and field data, preparing reinforced concrete layouts, analyzing structural frames, and designing columns, beams, slabs, and footings. Computer programs like STAAD and in-house software are used to aid in analysis and design. Designers are advised to be familiar with relevant Indian code provisions and follow the guidelines to independently complete reinforced concrete designs for buildings.

Strength of materials_I

This document provides an introduction to strength of materials, including concepts of stress, strain, Hooke's law, stress-strain relationships, elastic constants, and factors of safety. It defines key terms like stress, strain, elastic limit, modulus of elasticity, and ductile and brittle material behavior. Examples of stress and strain calculations are provided for basic structural elements like rods, bars, and composite structures. The document also covers compound bars, principle of superposition, and effects of temperature changes.

Presentation_on_Cellwise_Braced_frames

This presentation discusses the seismic response of cellwise concentrically braced frames. It introduces cellwise braced frames as a structural system that provides lateral stability through bracing elements arranged in cells within each bay. The document describes a study that analyzed 5 bay, 12 story reinforced concrete frames with different bracing configurations, including single-cell, two-cell, and three-cell arrangements. The study found that single-cell A-braced frames provided the highest material cost savings of up to 9.59% compared to bare frames. Two-cell and three-cell configurations further improved cost savings but required additional bracing. Overall, the study shows that optimally arranged cellwise braced frames produce a stiff, strong and econom

Study of MORT_&_H

The document provides an overview of the Ministry of Road Transport and Highways (MoRTH) in India. It discusses the ministry's role in formulating policies and regulations related to road transport. It outlines the ministry's history and organizational structure. It also summarizes some of the key specifications issued by MoRTH related to road and bridge construction, including specifications for earthworks, pavement layers, drainage, and other aspects of road projects. The document thus provides a high-level introduction to MoRTH and the specifications it issues for road development and transport in India.

List of various_IRCs_&_sps

The Indian Road Congress (IRC) was established in 1934 on the recommendations of the Jayakar Committee to oversee road development in India. It is the apex body for highway engineers and professionals. IRC has over 16,700 members from both public and private sector organizations involved in roads. It aims to promote standard specifications and best practices for road and bridge construction through various technical committees. It has published over 100 codes of practice and guidelines and oversees research activities through its Highway Research Board.

Analysis of multi storey building frames subjected to gravity and seismic loa...

This document summarizes a study on the seismic response of reinforced concrete frames with varying numbers of bays and storeys. Three frame configurations - 3 bay, 5 bay, and 7 bay with 9 stories each - were modeled and analyzed under gravity and seismic loads. Both prismatic frames and frames with non-prismatic elements like stepped beams and haunches at beam-column joints were considered. The effects of variables like haunch size, beam inertia, and live load patterns on internal forces and storey drift were examined. Key results showed that non-prismatic elements can reduce bending moments and axial forces compared to conventional prismatic frames.

Seismic response of _reinforced_concrete_concentrically_a_braced_frames

This document discusses the seismic response of reinforced concrete concentrically braced frames. It analyzes numerically various bracing patterns for a 5-bay 12-story building, including bare frames, fully braced frames, and partially braced frames with bracing applied at the bay-level or level-wise. Optimum bracing patterns are identified that reduce internal forces in columns and provide economic savings compared to bare frames or fully braced frames. Graphs show variations in axial, shear and bending forces for different bracing patterns, identifying patterns that fall within acceptable ranges. Savings of up to 7.87% are achieved with the optimum bracing patterns.

Use of mechanical_splices_for_reinforcing_steel

The document discusses the use of mechanical splices (couplers) as an alternative to traditional lap splicing for reinforcing steel. It provides details on different types of couplers, including threaded couplers. Experimental testing showed that couplers achieved similar or higher yield and ultimate stresses as compared to normal and welded reinforcing bars. While ductility was slightly reduced, factors like epoxy injection and staggered splicing can improve ductility. A cost analysis found that couplers provide significant cost savings over lap splices due to reduced steel requirements. Therefore, the study concludes that mechanical splices are an effective and economic replacement for lap splices.

Guide lines bridge_design

This document provides guidelines for bridge design in the Public Works Department. It introduces the contents and chapters, which cover aspects of bridge design, components, innovative structures, preparation of bridge projects, and other topics. The guidelines are intended to help engineers understand the department's practices for bridge design. The second edition was revised with new chapters and information to aid both new and experienced engineers.

Seismic response of cellwise braced reinforced concrete frames

The document analyzes the seismic response of reinforced concrete frames with different patterns of reinforced concrete bracing. Numerical models of 5-bay, 12-story reinforced concrete frames were analyzed with different bracing configurations including bare frames, fully braced, partially braced, outrigger braced, and cellwise braced. The responses, including internal forces, displacements, and member sizes, were compared for each configuration. Optimal baywise and levelwise locations for bracing were identified based on producing smaller internal forces within acceptable ranges. Cellwise bracing was explored as a configuration that combines advantages of other patterns while allowing for clear openings.

Chaper wise qpapers_bce

1. The document contains a question bank for the Basic Civil Engineering section covering topics like introduction to civil engineering, surveying, linear measurements, bearing, and leveling.
2. It includes 36 questions on surveying topics like chain surveying, compass surveying, and leveling with multiple parts and variations. Calculations and sketches are required to solve some questions.
3. The leveling questions provide staff readings and require entering data in a standard leveling table, calculating reduced levels using different methods, and applying arithmetic checks.

Basic Loads Cases

The document defines various types of loads that should be considered in structural analysis, including dead loads, live loads, wind loads, and earthquake loads. It provides details on how to apply these loads in both positive and negative directions of the X and Z axes. It also lists load combinations that should be analyzed according to Indian standards, including combinations for limit states of collapse and serviceability. The load combinations include factors for dead, live, wind, and earthquake loads.

Earthquake analysis by Response Spectrum Method

This document provides steps for performing an earthquake analysis using the response spectrum method in STAAD v8i. Key steps include:
1. Generating primary load cases for the X and Z directions using the specified code spectrum
2. Modeling dead and live loads
3. Obtaining support reactions for a load combination of dead + 0.25 live loads
4. Exporting the support reaction values to Excel tables
5. Importing the Excel tables back into STAAD as joint loads to apply the earthquake loads
6. Analyzing the structure with fixed supports instead of pin supports
The overall process applies earthquake loads to the structure using the response spectrum method and obtains the response of the structure under seismic loading

Earthquake analysis by psudeo static method

This document provides instructions for performing an earthquake analysis on a structure using the pseudo-static method in STAAD v8i. The steps include:
1. Defining the seismic parameters by adding a seismic definition and inputting values for the zone, response factor, importance factor, etc. based on IS 1893:2002.
2. Creating earthquake load cases in the X and Z directions and combining them with dead and live loads.
3. Assigning pin supports and obtaining support reactions for analysis.
4. Importing the support reaction values into Excel to create weight tables that are then input back into STAAD.
5. Removing the pin supports and assigning fixed supports at the foundation before running the full analysis

Basic Civil Engineering MCQ

The document contains a 58 question multiple choice test on basic civil engineering. The test covers topics such as surveying, building construction materials and techniques, structures, and other basic civil engineering concepts. The questions assess knowledge of concepts like types of surveying, building components, properties of materials like concrete and masonry, earthquake resistance techniques, and more.

PROBLEMS ON BEARINGS

1. The document provides examples of problems involving bearings observed in closed traverse surveys. It discusses calculating included angles, checking for angular errors, and correcting bearings based on lines assumed to be free from local attraction effects.
2. The first example shows calculations for a traverse with station positions, observed fore and back bearings, differences between bearings, included angles, and corrected bearings and stations free from attraction.
3. Several multi-part problems are presented involving calculating included angles from observed bearings, checking for errors, correcting bearings, and identifying stations free from local attraction for closed traverses. Step-by-step working is demonstrated for one example.

Transportation engineering

Transportation engineering

Chapter wise question papers_bce

Chapter wise question papers_bce

Design of staircase_practical_example

Design of staircase_practical_example

Presentation "Use of coupler Splices for Reinforcement"

Presentation "Use of coupler Splices for Reinforcement"

Guidelines_for_building_design

Guidelines_for_building_design

Strength of materials_I

Strength of materials_I

Presentation_on_Cellwise_Braced_frames

Presentation_on_Cellwise_Braced_frames

Study of MORT_&_H

Study of MORT_&_H

List of various_IRCs_&_sps

List of various_IRCs_&_sps

Analysis of multi storey building frames subjected to gravity and seismic loa...

Analysis of multi storey building frames subjected to gravity and seismic loa...

Seismic response of _reinforced_concrete_concentrically_a_braced_frames

Seismic response of _reinforced_concrete_concentrically_a_braced_frames

Use of mechanical_splices_for_reinforcing_steel

Use of mechanical_splices_for_reinforcing_steel

Guide lines bridge_design

Guide lines bridge_design

Seismic response of cellwise braced reinforced concrete frames

Seismic response of cellwise braced reinforced concrete frames

Chaper wise qpapers_bce

Chaper wise qpapers_bce

Basic Loads Cases

Basic Loads Cases

Earthquake analysis by Response Spectrum Method

Earthquake analysis by Response Spectrum Method

Earthquake analysis by psudeo static method

Earthquake analysis by psudeo static method

Basic Civil Engineering MCQ

Basic Civil Engineering MCQ

PROBLEMS ON BEARINGS

PROBLEMS ON BEARINGS

People as resource Grade IX.pdf minimala

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Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...

Medical image analysis has witnessed significant advancements with deep learning techniques. In the domain of brain tumor segmentation, the ability to
precisely delineate tumor boundaries from magnetic resonance imaging (MRI)
scans holds profound implications for diagnosis. This study presents an ensemble convolutional neural network (CNN) with transfer learning, integrating
the state-of-the-art Deeplabv3+ architecture with the ResNet18 backbone. The
model is rigorously trained and evaluated, exhibiting remarkable performance
metrics, including an impressive global accuracy of 99.286%, a high-class accuracy of 82.191%, a mean intersection over union (IoU) of 79.900%, a weighted
IoU of 98.620%, and a Boundary F1 (BF) score of 83.303%. Notably, a detailed comparative analysis with existing methods showcases the superiority of
our proposed model. These findings underscore the model’s competence in precise brain tumor localization, underscoring its potential to revolutionize medical
image analysis and enhance healthcare outcomes. This research paves the way
for future exploration and optimization of advanced CNN models in medical
imaging, emphasizing addressing false positives and resource efficiency.

Curve Fitting in Numerical Methods Regression

Curve Fitting

Comparative analysis between traditional aquaponics and reconstructed aquapon...

The aquaponic system of planting is a method that does not require soil usage. It is a method that only needs water, fish, lava rocks (a substitute for soil), and plants. Aquaponic systems are sustainable and environmentally friendly. Its use not only helps to plant in small spaces but also helps reduce artificial chemical use and minimizes excess water use, as aquaponics consumes 90% less water than soil-based gardening. The study applied a descriptive and experimental design to assess and compare conventional and reconstructed aquaponic methods for reproducing tomatoes. The researchers created an observation checklist to determine the significant factors of the study. The study aims to determine the significant difference between traditional aquaponics and reconstructed aquaponics systems propagating tomatoes in terms of height, weight, girth, and number of fruits. The reconstructed aquaponics system’s higher growth yield results in a much more nourished crop than the traditional aquaponics system. It is superior in its number of fruits, height, weight, and girth measurement. Moreover, the reconstructed aquaponics system is proven to eliminate all the hindrances present in the traditional aquaponics system, which are overcrowding of fish, algae growth, pest problems, contaminated water, and dead fish.

4. Mosca vol I -Fisica-Tipler-5ta-Edicion-Vol-1.pdf

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AT MBB AIRPORT

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Introduction, Modeling Concepts and Class Modeling: What is Object orientation? What is OO development? OO Themes; Evidence for usefulness of OO development; OO modeling history. Modeling
as Design technique: Modeling, abstraction, The Three models. Class Modeling: Object and Class Concept, Link and associations concepts, Generalization and Inheritance, A sample class model, Navigation of class models, and UML diagrams
Building the Analysis Models: Requirement Analysis, Analysis Model Approaches, Data modeling Concepts, Object Oriented Analysis, Scenario-Based Modeling, Flow-Oriented Modeling, class Based Modeling, Creating a Behavioral Model.

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Electric vehicle and photovoltaic advanced roles in enhancing the financial p...

Climate change's impact on the planet forced the United Nations and governments to promote green energies and electric transportation. The deployments of photovoltaic (PV) and electric vehicle (EV) systems gained stronger momentum due to their numerous advantages over fossil fuel types. The advantages go beyond sustainability to reach financial support and stability. The work in this paper introduces the hybrid system between PV and EV to support industrial and commercial plants. This paper covers the theoretical framework of the proposed hybrid system including the required equation to complete the cost analysis when PV and EV are present. In addition, the proposed design diagram which sets the priorities and requirements of the system is presented. The proposed approach allows setup to advance their power stability, especially during power outages. The presented information supports researchers and plant owners to complete the necessary analysis while promoting the deployment of clean energy. The result of a case study that represents a dairy milk farmer supports the theoretical works and highlights its advanced benefits to existing plants. The short return on investment of the proposed approach supports the paper's novelty approach for the sustainable electrical system. In addition, the proposed system allows for an isolated power setup without the need for a transmission line which enhances the safety of the electrical network

Advanced control scheme of doubly fed induction generator for wind turbine us...

This paper describes a speed control device for generating electrical energy on an electricity network based on the doubly fed induction generator (DFIG) used for wind power conversion systems. At first, a double-fed induction generator model was constructed. A control law is formulated to govern the flow of energy between the stator of a DFIG and the energy network using three types of controllers: proportional integral (PI), sliding mode controller (SMC) and second order sliding mode controller (SOSMC). Their different results in terms of power reference tracking, reaction to unexpected speed fluctuations, sensitivity to perturbations, and resilience against machine parameter alterations are compared. MATLAB/Simulink was used to conduct the simulations for the preceding study. Multiple simulations have shown very satisfying results, and the investigations demonstrate the efficacy and power-enhancing capabilities of the suggested control system.

An improved modulation technique suitable for a three level flying capacitor ...

This research paper introduces an innovative modulation technique for controlling a 3-level flying capacitor multilevel inverter (FCMLI), aiming to streamline the modulation process in contrast to conventional methods. The proposed
simplified modulation technique paves the way for more straightforward and
efficient control of multilevel inverters, enabling their widespread adoption and
integration into modern power electronic systems. Through the amalgamation of
sinusoidal pulse width modulation (SPWM) with a high-frequency square wave
pulse, this controlling technique attains energy equilibrium across the coupling
capacitor. The modulation scheme incorporates a simplified switching pattern
and a decreased count of voltage references, thereby simplifying the control
algorithm.

Embedded machine learning-based road conditions and driving behavior monitoring

Car accident rates have increased in recent years, resulting in losses in human lives, properties, and other financial costs. An embedded machine learning-based system is developed to address this critical issue. The system can monitor road conditions, detect driving patterns, and identify aggressive driving behaviors. The system is based on neural networks trained on a comprehensive dataset of driving events, driving styles, and road conditions. The system effectively detects potential risks and helps mitigate the frequency and impact of accidents. The primary goal is to ensure the safety of drivers and vehicles. Collecting data involved gathering information on three key road events: normal street and normal drive, speed bumps, circular yellow speed bumps, and three aggressive driving actions: sudden start, sudden stop, and sudden entry. The gathered data is processed and analyzed using a machine learning system designed for limited power and memory devices. The developed system resulted in 91.9% accuracy, 93.6% precision, and 92% recall. The achieved inference time on an Arduino Nano 33 BLE Sense with a 32-bit CPU running at 64 MHz is 34 ms and requires 2.6 kB peak RAM and 139.9 kB program flash memory, making it suitable for resource-constrained embedded systems.

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Certificates - Mahmoud Mohamed Moursi Ahmed

Certificates - Mahmoud Mohamed Moursi-Ahmed

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Software Engineering and Project Management - Introduction, Modeling Concepts...

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Electric vehicle and photovoltaic advanced roles in enhancing the financial p...

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An improved modulation technique suitable for a three level flying capacitor ...

Embedded machine learning-based road conditions and driving behavior monitoring

Embedded machine learning-based road conditions and driving behavior monitoring

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Properties Railway Sleepers and Test.pptx

哪里办理(csu毕业证书)查尔斯特大学毕业证硕士学历原版一模一样

哪里办理(csu毕业证书)查尔斯特大学毕业证硕士学历原版一模一样

原版制作(Humboldt毕业证书)柏林大学毕业证学位证一模一样

原版制作(Humboldt毕业证书)柏林大学毕业证学位证一模一样

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Seminar on Distillation study-mafia.pptx

Certificates - Mahmoud Mohamed Moursi Ahmed

Certificates - Mahmoud Mohamed Moursi Ahmed

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Software Quality Assurance-se412-v11.ppt

- 1. CHAPTER NO.7 CIRCULAR MOTION 7.1 Projectile Motion (an example of circular motion) Terms: 7.1.1 Projectile (Nothing but particle): It is a particle or object projected in the space at an inclination to the direction of gravity, moving under the combined effect of vertical and horizontal forces. 1) Trajectory: It is a path, traced by a projectile in the space. 2) Point of Projection: It is the initial point of the particle (see Fig. 1 Point A) 3) Angle of inclination or Projection: The angle, with a horizontal, at which a projectile is projected (see Fig. 1) 4) Horizontal Range or Range (R) : The distance between the point of projection and the point where projectile strikes the ground (see Fig. 1) 5) Time of Flight: The total time taken by the projectile, to reach the maximum height i.e. hmax and to return back to the ground. 6) Velocity of projection: The velocity with which, a projectile is projected (see Fig. 1) Chapter No. 7 Circular Motion Page 1
- 2. Fig. 1 7.2 Study of a projectile: 1) Generally, the velocity of the projection ‘u’ split up in to or resolved into two components ‘u cos α’ and ‘u sin α’. i. e. Vertical component V = u sin α and Horizontal component H = u cos α 2) The component in vertical direction is subjected to retardation due to gravity. Therefore, this vertical velocity ‘u sin α’ is subjected to retardation for first half of trajectory before attaining maximum height i.e. hmax and for second half it is subjected to acceleration due to gravity, before coming to rest. 3) The component in horizontal direction, there is no retardation or acceleration due to gravity. Therefore, this horizontal velocity ‘u cos α’ is remain constant throughout the motion. For first half of trajectory ---------- { 푣 = 푢 sin 훼 − 푔푡 푣 2 = 푢2 sin2 훼 − 2푔푠 푠 = ( 푢 sin 훼 ) 푡 − (1 2 푔 푡2) Chapter No. 7 Circular Motion Page 2
- 3. For second half of trajectory ---------- { 푣 = 푢 sin 훼 + 푔푡 푣2 = 푢2 sin2 훼 + 2푔푠 푠 = ( 푢 sin 훼 ) 푡 + (1 2 푔 푡2) 4) Thus, the time taken by the body or particle or projectile to reach the ground, is calculated by vertical component (u sin α ) of the velocity and the horizontal component of the velocity ( u cos α). 5) Mathematically, 퐻표푟푖푧표푛푡푎푙 푅푎푛푔푒 (푅) [ 표푟 퐻표푟푖푧표푛푡푎푙 퐷푖푠푡푎푛푐푒 퐶표푛푠푡푎푛푡 퐻표푟푖푧표푛푡푎푙 푣푒푙표푐푖푡푦 ] = [ (푢 cos 훼 ) 푇푖푚푒 (푡) ] 푥 [ ] Fig. 2 7.3 Derivation of the expression or equation for the path of a projectile: Consider a particle projected upward from point A, at an angle α, with the horizontal, with an initial velocity u m/s as shown in Fig. 1 below. Now, the velocity of projection u can be split up into two components i.e. u cos α and u sin α. Chapter No. 7 Circular Motion Page 3
- 4. Fig. 3 Consider any point as the position of the particle, after time t seconds with co-ordinates x and y as shown in Fig. 1 푦 = ( 푢 sin 훼 ) 푡 − (1 2 푔 푡2) ------------------- (1) And 푥 = ( 푢 cos 훼 ) 푡 ----------- (2) Therefore, 푡 = 푥 푢 cos 훼 Substituting in (1) 푦 = ( 푢 sin 훼 ) 푥 푢 cos 훼 − ( 1 2 푔 푥2 ) 푢2 cos2 훼 푦 = 푥 tan 훼 − 푔 푥2 2 푐표푠2 푢2 ---------- (3) Equation (3) is known as equation of trajectory 7.4 Derivation of expression for the time of flight of the projectile on a horizontal plane: We have, 푠 = 푢푡 + 1 2 푎 푡2 Chapter No. 7 Circular Motion Page 4
- 5. 푦 = ( 푢 sin 훼 ) 푡 − (1 2 푔 푡2) ------------------- (1) i.e. s = y, u = u sin α and a = g When the projectile p is at point B, y = 0 Substituting, the value of y in eqn (1) 0 = ( 푢 sin 훼 ) 푡 − ( 1 2 푔 푡2) ( 푢 sin 훼 ) 푡 = ( 1 2 푔 푡2) ( 푢 sin 훼 ) = ( 1 2 푔 푡) 푡 = 2 푢 sin 훼 푔 i.e. 1) time required to reach the maximum height 푡 2 = 푢 sin 훼 푔 Chapter No. 7 Circular Motion Page 5
- 6. 7.5 Derivation of the expression for horizontal range (R) of the projectile: We know, Horizontal component of velocity = u cos α And Time of flight, 푡 = 2 푢 sin 훼 푔 Therefore, [Horizontal range ] = [퐻표푟푖푧표푛푡푎푙 푣푒푙표푐푖푡푦] 푥 [Time of flight] = [u cos α] 푥 [2 푢 sin 훼 푔 ] 푅 = sin 2 훼 푢2 푔 Note: The range will be maximum when sin 2α = 1 Chapter No. 7 Circular Motion Page 6
- 7. 2α = 900 α = 450 Rmax = 푢2 푔 7.6 Derivation of expression for the maximum height of a projectile on a horizontal plane: We have, the vertical component of initial velocity u is v = u sin α and vertical component of final velocity v = 0 Therefore, Average velocity = 푢 sin 훼 +0 2 = 푢 sin 훼 2 Now, [푣푒푟푡푖푐푎푙 푑푖푠푡푎푛푐푒] = [퐴푣푒푟푎푔푒 푣푒푟푡푖푐푎푙 푣푒푙표푐푖푡푦] x [푡푖푚푒] Chapter No. 7 Circular Motion Page 7
- 8. = 푢 sin 훼 2 푥 푢 sin 훼 푔 = 푠푖푛2 훼 푢2 2 푔 Where, 푢 sin 훼 푔 = is the time required by the projectile to reach the maximum height H = 푠푖푛2 훼 푢2 2 푔 Questions:- 1. A projectile is fired upwards at an angle of 300 with a velocity of 40 m/s. Calculate the time taken by the projectile to reach the ground after firing. 2. If a particle is projected inside a horizontal tunnel which is 5 m high with a velocity of 60 m/s, find the angle of projection and the greatest possible range. 3. The range of projectile on a horizontal plane is 240 m and the time of flight is 8 sec. Find the initial velocity and the angle of projection. 4. A body is projected at such an angle that the horizontal range is three times the greatest height. Find the angle of projection. 5. Find the least initial velocity which a projectile may have, so that it may clear a wall 3.6 m high and 4.8 m distant (from the point of projection) and strike the horizontal plane through the foot of the wall at a distance 3.6 m beyond the wall. The point of projection is at the same level as the wall. 6. Find the angle of projection at which the horizontal range and the maximum height of a projectile are equal. May 2010 (06 MKS) 7. A particle is projected in air with a velocity 100 m/s and at an angle of 300 with the horizontal. Find: 1) The horizontal range 2) The maximum height by the particle 3) And the time of flight Ans: R = 882.8 m, Hmax = 127.42 m, t = 10.19 sec Chapter No. 7 Circular Motion Page 8
- 9. 8. A projectile is fired with an initial velocity of 250 m/s at a target located at a horizontal distance of 4 km and the vertical distance of 700 m above the gun. Determine the value of firing angle to hit the target. (Neglect air resistance). Ans: α = 68.820 and 31.080 9. A projectile is aimed to a mark on a horizontal plane through the point of projection and fall 12 m short of the mark and with an angle of projection 150. While it overshoots the mark by 24 m when the angle of projection to hit the mark. Assume no air resistance. Take the velocity of projection is constant in all cases. Ans: R = 48 m, u = 26.57 m, α = 20.550 Case I) Projectile projected horizontally from certain height a) Considering vertical motion of projectile We have, S = 퐮퐭 + ퟏ ퟐ 퐚퐭ퟐ Here, S = y = vertically downward displacement u = initial velocity = u sin α = 0 a = acceleration due to gravity = g = 9.81 m/s2 ∴ y = ퟏ ퟐ 퐠 퐭ퟐ---------- (1) b) Considering horizontal motion of projectile [Horizontal range ] = [퐻표푟푖푧표푛푡푎푙 푣푒푙표푐푖푡푦] 푥 [Time of flight] x = u x t --------- (2) Chapter No. 7 Circular Motion Page 9
- 10. Problems: 1) An aircraft moving horizontally at a speed of 1000 kmph at a height of 1500 m releases a bomb which hits the target. Find: 1) Time required for the bomb to reach the target on ground 2) The horizontal distance of the aircraft from the target when it releases the bomb. (May 2007 8 MKS) Ans: t = 17.49 sec and x = 4857.66 m 2) Solve the same problem when y = 2000 m and u = 150 m/s. Ans: t = 20.2 sec and x = 3030m 3) Find out u = ? when y = 100 m and x = 200 m Ans: t = 4.515 sec and u = 44.3 m/s 4) Find y = ? and u = ? when time required to strike the ground is 15 sec when x = 50 m. Ans: y = 1103.625 m and u = 3.33 m/s 5) A person wants to jump over a ditch as shown in Fig. below. Find the max. velocity with which he should jump? (May 2006 6 MKS) Ans: t = 0.638 sec and u = 4.702 m/s Chapter No. 7 Circular Motion Page 10
- 11. Case II) Projectile projected at an angle α from certain height (say y) a) Considering vertical motion of projectile We have, S = 퐮퐭 + ퟏ ퟐ 퐚퐭ퟐ Here, S = y = vertically downward displacement u = initial vertical velocity = u sin α = 0 a = acceleration due to gravity = g = 9.81 m/s2 ∴ − y = (u sin α) – ퟏ ퟐ 퐠 퐭ퟐ y = - (u sin α) + ퟏ ퟐ 퐠 퐭ퟐ---------- (1) b) Considering horizontal motion of projectile [Horizontal range ] = [퐻표푟푖푧표푛푡푎푙 푣푒푙표푐푖푡푦] 푥 [Time of flight] x = u cos α x t --------- (2) Velocity with which it strikes the ground (VB): VB = u = initial velocity Chapter No. 7 Circular Motion Page 11
- 12. VH = u cos α VV = u sin α We have, 퐯 = 퐮 + 퐚퐭 -VV = u sin α – gt VV = -u sin α + gt ퟐ + 푽푽 VB = √ 푽푯 ퟐ--------------- (velocity of hit) Direction of hit: θ = tan-1 ( 푽푽 푽푯 ) ------------ (with the horizontal) Problems: 1. A body is projected from the top of the tower 40 m high and strikes the ground after 10 seconds at a point 400 m from the base of the tower. Determine the velocity and angle of projection. Also determine the maximum height attained by the body above ground level. Dec. 2009 (10 MKS) Ans: u = 60.24 m/s and Hmax = 143.43 m 2. A cricket ball is thrown by a fielder from a height of 2 , at an angle of elevation 300 to the horizontal with an initial velocity of 20 m/s, hits the wickets at a height of 0.5 m from the ground. How far the fielder from the wicket? (May 2004 12 MKS) Ans: t = 2.181 sec, x = 37.77 m 3. A solider fires a bullet at an angle of elevation 300 from his position on the top of hill to strike a target which is 60 m lower than the position of the solider. The initial velocity of the bullet is 75 m/s. Calculate: a) Hmax to which bullet rise above horizontal b) The actual velocity with which it will strike the target c) Total time required by for the flight of the bullet Chapter No. 7 Circular Motion Page 12
- 13. Ans: Hmax = 131.74 m, t = 9.01 sec, vB = 82.456 m/s, θ = 38.020 4. A projectile fired from the edge of a 150 m high cliff with an initial velocity of 180 m/s at an angle of elevation of 300 with the horizontal. Neglecting air resistance. Find: 1) The greatest elevation above the ground reached by the projectile and 2) Horizontal distance from gun to the point, where the projectile strikes the ground. Ans: Hmax = 563.3 m, t = 19.9 sec, R = 3.012 km Case III) Projectile projected at an angle α from certain height to the downward (say y) c) Considering vertical motion of projectile We have, S = 퐮퐭 + ퟏ ퟐ 퐚퐭ퟐ Here, S = - y = vertically downward displacement u = initial vertical velocity = - u sin α a = acceleration due to gravity = - g = 9.81 m/s2 ∴ − y = ( - u sin α) – ퟏ ퟐ 퐠 퐭ퟐ y = (u sin α) + ퟏ ퟐ 퐠 퐭ퟐ---------- (1) d) Considering horizontal motion of projectile [Horizontal range ] = [퐻표푟푖푧표푛푡푎푙 푣푒푙표푐푖푡푦] 푥 [Time of flight] Chapter No. 7 Circular Motion Page 13
- 14. x = u cos α x t --------- (2) Velocity with which it strikes the ground (VB): VB = u = initial velocity VH = u cos α VV = u sin α We have, 퐯 = 퐮 + 퐚퐭 -VV = - u sin α – gt VV = u sin α + gt ퟐ + 푽푽 VB = √ 푽푯 ퟐ--------------- (velocity of hit) Direction of hit: θ = tan-1 ( 푽푽 푽푯 ) ------------ (with the horizontal) Problems: 1) A stone is thrown from the top of the tower 30 m high at an angle of 400 with horizontal with velocity 40 kmph. Find when and where the stone will hit a horizontal ground. Also find the velocity and direction of striking. Ans: t = 1.85 sec, x = 15.74 m, Vb = 26.67 m/s, θ = 71.390 Chapter No. 7 Circular Motion Page 14