Applied 40S May 4, 2009
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This document provides examples of vector problems and instructions for solving them using the parallelogram method. It includes problems about airplanes traveling at various speeds and directions, ships moving with currents, forces on objects, velocities of objects moving and rebounding, and comparing vector quantities between two locations. Readers are instructed to show their work and use diagrams to solve the problems.
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Similar to Applied 40S May 4, 2009
Applied Math 40S April 25, 2008
This document contains instructions and questions for a vectors pre-test, including:
1) A question about determining the direction and speed of a ship traveling at 40° in still water with a current of 6 knots at 340° pushing it.
2) A question about calculating the direction and distance an airplane must travel to return to its starting point after traveling for an hour at 250 km/h at 30° north of west and then for 40 minutes at 300 km/h at 42° east of north.
3) A question about finding the resultant force of three forces acting on a body: 30 N at 50° west of north, 45 N at 30° north of east, and 50 N southeast.
Applied Math 40S Slides April 23, 2007
This document provides instructions to summarize five vectors problems by drawing scale diagrams labeling the vectors, scales, and calculations. The problems include a person walking, a boat traveling at an angle, an ultralite plane with wind resistance, two people kicking a soccer ball at angles, and an aircraft with wind resistance. Students are to solve for the resultant vectors and directions in each case.
Applied Math 40S April 23, 2008
The document describes how to use the TRISOLVE program on a scientific graphing calculator to solve vector problems involving distance, direction, speed, and wind. It provides 3 example problems - finding the distance and direction from a starting point after walking north, east, and south; calculating the velocity of an airplane factoring in its airspeed, heading, and a jet stream; and determining the groundspeed and direction of an aircraft given its speed, bearing, and a crosswind. The TRISOLVE program can be used to solve similar vector problems involving movement over distance and combined speeds and directions.
Real Life Applications of Vector Mathematics
1. The document discusses several examples of applying vector concepts, such as a stone being thrown from a moving train, holding an umbrella at an angle to protect from rain while running, and calculating the resulting velocity of an aircraft moving in different directions and speeds.
2. Vectors are used in gaming to represent positions, directions, and velocities of objects like a character's position and a plane's movement.
3. In football, the quarterback must calculate the speed and direction of a pass to the receiver as a vector, taking into account both the quarterback and receiver's speeds and directions of movement. An example problem is given of calculating the angle the quarterback must throw the ball to hit a stationary receiver downfield.
Day 4 and 5 applications worked
This document contains examples of navigation and force problems involving boats, airplanes, and objects on inclined planes. It begins with an explanation of bearing measured in degrees from North. The remainder of the document provides 9 examples of navigation and force problems, such as calculating the distance and bearing traveled by boats moving at different speeds and directions, finding the component form and ground speed of airplanes in the presence of wind, and determining the horizontal and vertical forces needed to push objects up inclined planes at various angles. It concludes by listing additional homework problems from pages 434 and 512.
9 5 applications to navigation and surveying
This document discusses using trigonometry to solve navigation and surveying problems. It defines course as the angle from north of a ship or plane's direction of travel, and compass bearings as the angle from one location to another. Two example problems are given: one calculating the distance a ship travels over two legs at different courses and speeds, and another finding the bearing and distance between two locations given their positions relative to a third location. A practice problem is presented asking the reader to calculate the total distance traveled by a plane over three legs with different courses.
Relative Velocity by UK Physics
The document discusses relative velocity between two moving bodies. It defines relative velocity as the velocity of one body as seen from another body in motion. The relative velocity of body A with respect to body B is given by VA - VB, where VA and VB are the velocities of bodies A and B, respectively. The document provides examples of calculating relative velocity in one and two dimensions. It also discusses problems related to crossing a river and calculating velocity for different scenarios. Homework questions involving calculating relative velocities in various situations are provided at different levels.
vectorshonors.ppt
The document describes scalar and vector quantities in physics. Scalars have magnitude only, while vectors have both magnitude and direction. The document discusses how to add and subtract vectors by combining their components and provides examples. It also covers using trigonometry to calculate resultant vectors when vectors are perpendicular, including finding the direction angle.
vectorshonors in Physique Better titles and descriptions lead to more readers
The document defines scalar and vector quantities in physics. Scalars have magnitude only, while vectors have both magnitude and direction. The document discusses how to add and subtract vectors by combining their components. It also explains how to use trigonometry to calculate the resultant of two vectors that are not collinear, including finding the direction angle. Examples are provided for applying these vector concepts to problems involving displacement, velocity, and other physical quantities.
vectors.ppt
Vectors have both magnitude and direction, while scalars have only magnitude. Common vector quantities include velocity, acceleration, and displacement. Vectors are represented by arrows with length proportional to magnitude and pointing in the direction of the vector. Vector addition and subtraction use a head-to-tail method, while the Pythagorean theorem is used when vectors are perpendicular. Examples demonstrate calculating resultant displacements and velocities from component vectors using trigonometric functions like sine, cosine, and tangent.
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Vectors have both magnitude and direction, while scalars have only magnitude. Common vector quantities include velocity, acceleration, and displacement. Vectors are represented by arrows with length proportional to magnitude and pointing in the direction of the vector. Vector addition and subtraction use a head-to-tail method, while the Pythagorean theorem is used when vectors are perpendicular. Examples demonstrate calculating resultant displacements and velocities from component vectors using trigonometric functions like sine, cosine, and tangent.
vectors
Vectors have both magnitude and direction, while scalars have only magnitude. Common vector quantities include velocity, acceleration, and displacement. Vectors are represented by arrows with length proportional to magnitude and pointing in the direction of the vector. Vector addition and subtraction are done by drawing the vectors head to tail. When vectors are perpendicular, the Pythagorean theorem is used to find the resultant. Vector components can be found using trigonometric functions like sine and cosine. Examples demonstrate calculating displacements, velocities, and components from descriptions of motions involving multiple vectors.
maths project.pptx
Vectors have both magnitude and direction, while scalars have only magnitude. Vectors can be added or subtracted by drawing them head to tail. When vectors are perpendicular, the Pythagorean theorem is used to find the resultant. Displacement problems involving vectors require calculating horizontal and vertical components using trigonometric functions like sine and cosine. Real-world examples demonstrate how to calculate the resultant displacement, velocity or other vector quantities when given multiple vectors in different directions.
KINEMATICS_Speed_Velocity_Acceleration.ppt
This document defines and explains key concepts related to motion including:
- Speed is distance traveled over time and does not indicate direction, while velocity includes both speed and direction.
- Acceleration is the rate of change of velocity over time and can be positive (speeding up) or negative (slowing down).
- Examples are provided to demonstrate how to calculate speed, velocity, acceleration, and displacement using basic kinematic equations.
Lecture 2 - Introduction to Vectors.pptx
This document defines scalar and vector quantities and provides examples of each. It explains that vectors have both magnitude and direction, while scalars only have magnitude. The document also outlines how to calculate the addition, subtraction, and perpendicular components of vectors using graphical representations and the Pythagorean theorem. Examples are provided for calculating displacements, velocities, and other vector quantities based on their components.
Vectors 03 Mar 20
This document provides instructions and problems for solving vector problems by drawing scale diagrams, adding vectors using the triangle method, and calculating distances and directions from starting points. Specifically, it asks the reader to: 1) draw scale diagrams of vectors for a person walking 13 blocks E15°S and a boat headed 300° at 45 km/h; 2) add the vectors using the triangle method; and 3) solve problems involving distances and directions for a man walking in different directions and a jogger moving north and east over time.
PLANE-TRIGONOMETRY.pptx
This document provides information on trigonometric functions of right triangles. It defines the sine, cosine, and tangent functions as ratios of sides of a right triangle. It also introduces cosecant, secant, and cotangent as reciprocals of the primary trig functions. Several examples are given to calculate unknown side lengths or angles using trig functions. The document then covers trigonometric identities, angle sum and difference formulas, double and half angle formulas, and techniques for reducing trig powers and converting between sum and product formulas. It concludes with information on measuring angles in different units and introduces the study of oblique triangles, including the Law of Sines and Law of Cosines.
PRECESSION-UNIT 1.pptx
1. Gyroscopes are devices used to control the orientation and angular velocity of rotating bodies. They use the principle of gyroscopic precession to maintain their orientation.
2. Common applications of gyroscopes include their use in inertial navigation systems, gyrocompasses, and to provide stability in vehicles like ships, airplanes, bicycles, and motorcycles.
3. The reactive gyroscopic couple experienced by rotating objects like the engines of airplanes and ships helps provide stability when turning. For example, when an airplane turns left, the reactive couple presses down on the right wing and lifts the left wing, counteracting the turning moment.
G7 Science Q3- Week 1_2- Force and Motion Standards.ppt
1) The document discusses force and motion standards related to determining the relationship between velocity and acceleration, and the effect of balanced and unbalanced forces on an object.
2) It defines key terms related to motion including distance, displacement, speed, velocity, and acceleration. Distance refers to how far an object travels regardless of direction, while displacement takes direction into account. Speed is how fast something moves, while velocity includes both speed and direction.
3) Acceleration is defined as the rate of change of velocity, whether that be a change in speed, direction, or both. Equations for calculating speed, velocity and acceleration from distance, time and other variables are provided.
mechanics
Mechanics deals with forces and motion, including kinetics, statics, and kinematics. Vector quantities like displacement and velocity have both magnitude and direction, while scalar quantities like mass and time only have magnitude. Mechanics also examines concepts like average speed, average velocity, acceleration, energy, heat, and the conservation of energy. Forces cause motion or changes in motion based on Newton's laws of motion.
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vectorshonors in Physique Better titles and descriptions lead to more readers
vectorshonors in Physique Better titles and descriptions lead to more readers
G7 Science Q3- Week 1_2- Force and Motion Standards.ppt
G7 Science Q3- Week 1_2- Force and Motion Standards.ppt
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Leading Change v1
“If you really want to understand something, try changing it.” - Kurt Lewin
As the Director of Learning for a school division made up of 18 schools, my job is to help lead the largest change initiative ever undertaken in our school community. One of the most important, difficult, messy things any school leader does is lead change. While we can learn from the change leadership of others, copying their work most often leads to failure. Success is more likely to come from adapting others work to our own context. In this workshop I share the journey we’ve undertaken collectively in our schools; how we developed a shared vision, cultivated collaborative cultures, maintained a focus on deep learning, and wrestle with the nuances of accountability. Informed by the latest research on change management in education, we also model strategies for fostering deep learning conversations in your schools. We’ll engage in some deeper learning conversations together and take back a wealth of ideas you can adapt to your own context. Developing collaborative cultures is careful and precise work that has profound impact when carried out well. So how do you do that? Come, let’s learn together. Good people are important, but good cultures are moreso.
Providing Permission To Wonder v2.1
In a world where knowledge is more a verb than a noun how do we foster deep learning in our students? Good questions cause thinking. Unfortunately, many of the questions regularly asked in classrooms focus on knowledge as a noun. This presentation will explore inquiry as a pedagogical stance and the effective use of thinking and learning tools in the classroom. We will work together to model teaching practices that lead to students co-constructing a networked (real world) rather than hierarchical (artificial) understanding of their world regardless of grade level or discipline.
Participants will leave this workshop with a toolkit of research based questioning and thinking strategies they can begin using with their students tomorrow.
Things That Suck About Digital Citizenship v1
The document is a presentation about digital citizenship given by Darren Kuropatwa at the Building Learning Communities Conference in Boston, MA in July 2017. It discusses the importance of digital citizenship and responding to adversity with persistent kindness. It provides examples of digital citizenship issues and scenarios for discussion. It encourages participants to think about their own digital footprint and how to be good digital citizens.
Digital Storytelling for Deeper Learning v1
Presented at the Riding the Wave Conference in Gimli, Manitoba. May 2017.
In two words, you remember the whole story: glass slipper, sour grapes, cold porridge. You remember more than facts, you recall relationships & deeper connections between characters. Some of the powerful ways we leverage digital for deeper learning includes challenging sources of information (fake news), exploring bias (developing empathy through multiple perspectives), and creating powerful feedback loops that foster deeper learning.
Powerful narratives, in a word or two, bring to mind a wealth of ideas & relationships; more than just facts. How can we find stories that make our teaching sticky and help kids find, and more importantly tell, stories that make learning stick? This workshop will equip teachers with the skills & knowledge to foster deeper learning across the curriculum by intentionally leveraging digital tools to foster deeper learning.
Tales of Learning and the Gifts of Footprints v4.2
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The Fourth Screen v4.2
Presented at the Richmond District Conference, Feb 2017.
A series of stories woven together to start a conversation with middle and high school students, teachers, and parents about living our lives on and offline (on The Fourth Screen) more thoughtfully.
This talk focuses primarily on the ideas of Empathy, Empowerment & Persistent Kindness and shares resources teachers can use to lead these sorts of conversations with their own students.
Making Student Thinking Visible v4
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A group of educators from the BYTE Conference 2017 (Build Your Teaching Experience) share their ideas about learning as a series of visual metaphors they found on their phones.
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Slides to support a master class on making student thinking visible through practical hands-on activities and structured around Dylan Wiliam's work on formative assessment and active learning.
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In a world where knowledge is more a verb than a noun how do we foster deep learning in our students? Good questions cause thinking. Unfortunately, many of the questions regularly asked in classrooms focus on knowledge as a noun. This presentation will explore the effective use of thinking and learning tools in the classroom. We will work together to model teaching practices that lead to students co-constructing a networked (real world) rather than hierarchical (artificial) understanding of their world regardless of grade level or discipline.
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Applied 40S May 4, 2009
- 1. Vectors Pre-Test which way? by flickr user aurevoirkatie
- 4. 26.604 N
- 6. (5) An airplane travels at a speed of 250 km/h in a direction 30° north of west for one hour. It then travels at a speed of 300 km/h for 40 minutes in a direction of 42° east of north. To return directly to its starting point, in what direction and what distance must the airplane travel? Show all work. Use the back of this page to answer this question. Remember, draw BIG diagrams.
- 8. Where Do I Want To Go? A ship needs to travel in the direction of 40°. The ship has a speed of 20 knots in still water. A current of six knots at 340° is pushing the ship. Determine the direction the ship is headed and the magnitude of the ship's resultant velocity.
- 9. An aircraft is flying at a rate of 600 km/h with a bearing of 60°. A 100 km/h wind is blowing in the direction of 270°. Calculate the groundspeed and direction of the aircraft. Round your answer to the nearest whole numbers.
- 10. A large black ant pulls a breadcrumb N32°E with a force of 0.03 N. A small red ant pulls with a 0.045 N force in the direction E5°S. Determine the magnitude and direction of the resultant force. 0.0644 N BEARING 70.48° HOMEWORK
- 11. An airplane is flying with a heading of 150° and an airspeed of 550 mph. The airplane is flying through a jet stream which is moving 175 mph with a heading of 80°. What is the velocity of HOMEWORK the airplane with respect to the ground?
- 12. The Parallelogram Method ... We use the parallelogram method when the vectors are arranged tail-to-tail. 5cm Scale: 1 cm = 2 km 3cm We find the quot;answerquot; by measuring the length of the resultant vector and it's bearing using a ruler and protractor. The length of the resultant vector often has to be converted to appropriate units using the given scale.
- 13. You try ... Add each pair of vectors using the parallelogram method. Find Find is 3 meters east is 3 meters southwest is 4 meters north is 4 meters west
- 14. A ball is thrown horizontally against a wall with a velocity of 10 m/s. It rebounds with a velocity that has a magnitude of 75% of the initial velocity. Sketch two vectors to represent the two velocities. Scale 1cm = 1m/s
- 15. Rhonda lives 5 km from Morris in a SW direction. Travis lives 5 km SW of Thompson. Are the two vector quantities equal? Explain.
- 16. Two ropes suspend a crate with a weight of 800N. The force exerted by one rope is 600N, directed to the left at an angle of 60° above the horizontal. What force is exerted by the other rope to keep the crate from moving?