This document describes a physics project on two-dimensional motion and projectile motion. It begins by outlining the objectives and previous knowledge of students. The content section then explains key concepts like two-dimensional and circular motion, the characteristics of a projectile, the different types of projectile motion including horizontal and oblique projectiles. Equations are provided for time of flight, maximum height, horizontal range, and frequently asked questions are listed at the end.

1. PHYSICS PROJECT
V.SHRIVASTAVA P.G.T. (PHYSICS)
Jawahar Navodaya Vidyalaya
Nowgong , Chhatarpur (M.P.)
PRESENTED BY

2.  OBJECTIVES
 1.TO KNOW ABOUT THE CONCEPT OF
TWO DIMENTIONAL MOTION.
 2.TO UNDERSTAND THE EFFECT OF
GRAVITY ON TWO DIMENTIONAL
MOTION.
 3.TO KNOW ABOUT THE TYPES OF
PROJECTILE MOTION IN NATURE.

3. PREVIOUS KNOWLEDGE
 1.STUDENTS KNOW ABOUT THE 1-D
MOTION.
 2.STUDENTS KNOW ABOUT EFFECT
OF GRAVITY IN 1-D MOTION.
 3.THEY ARE FAMILIAR ABOUT THE
TERM UNIFORM AND NONUNIFORM
MOTION.

4. CONTENT
. TWO DIMENSIONAL MOTION.
 EXAMPLES OF TWO DIMENSIONAL MO
TION
 DESCRIPTION OF CIRCULAR MOTION
 THE PROJECTILE.
 THE TYPES OF PROJECTILE MOTION.
 NATURE OF TRAJECTORY.
 TIME OF FLIGHT IN PROJECTILE MOTION.
 MAXIMUM HORIZONTAL RANGE.
 MAXIMUM HEIGHT.
 EXPRESSION FOR RESULTANT VELOCITY.

5. TWO DIMENTIONAL MOTION
 IF BODY MOVES ON A PLANE THEN
THE OF BODY IS KNOWN AS TWO
DIMENTIONAL MOTION
 EXAMPLES OF TWO DIMENTIONAL
MOTION
 (a) motion of a body in plane
 (b) circular motion
 (c) projectile motion

6. MOTION OF A BODY IN A PLANE

7. CONTD…

8. CONTD…

9. CONTD…

10. CONTD…

11. CIRCULAR MOTION
 IF A BODY MOVES IN A CIRCULAR
PATH THEN MOTION OF BODY IS
KNOWN AS CIRCULAR MOTION
 IN CIRCULAR MOTION THE ANGULAR
VELOCITY AND LINEAR SPEED BOTH
ARE CONSTANT BUT LINEAR
VELOCITY IS NOT CONSTANT.
HENCE THE CIRCULAR MOTION OF A
BODY IS AN ACCELERATED MOTION.

12. MOTION ON CIRCULAR PATH

13. DIGRAM OF CIRCULAR MOTION
p
c
P1
r
r
v1
v2

14. DESCRIPTION OF CIRCULAR
MOTION
 Let V1 be the initial velocity of the particle
 Let V2 be the velocity after time t.
 Let ω be the angular velocity of the particle.
 Let r be the radius of the circular path.
 During the motion of the particle in circular path
the direction of velocity is tangential to the
circular path and changes continuously due to
which the acceleration acts towards the centre of
the circular path.

15. The direction of acceleration &velocity is
shown below.
C
V
a

16. .Release of an arrow
from a bow.
CONTD…

17.  PROJECTILE:-An
object projected into
space or air, such
that it moves under
the effect of the
gravity alone is
called projectile.
 Examples:-1.Firing of
bullet from the gun.
CONTD…

18.  Throw of a stone
from the top of the
tower.
CONTD…

19.  Kicking of a football
into the air.
CONTD…

20. HORIZONTAL PROJECTILE
 If a body which is projected horizontally
from certain height with constant velocity
is known as horizontal projectile
The path of projectile is called trajectory
and
the nature of trajectory is parabolic.

21. DESCRIPTION OF PROJECTILE
MOTION
 Any object projected into space or air
such that it moves under the effect of
gravity alone is called projectile .The
motion of projectile is known as projectile
motion.
 TYPES OF PROJECTILE MOTION
(a) Horizontal projectile.
(b) Oblique projectile.

22. CONTD…

23. DESCRIPTION OF THE DIAGRAM
 THE VELOCITY ALONG X- AXIS IS
UNIFORM &THE VELOCITY ALONG Y-
AXIS IS NONUNIFORM OR
ACCELERATING MOTION.
 THE EQUATION OF HORIZONTAL
PROJECTILE IS Y =1/2 g (x/u)2.
 WHICH IS THE EQUATION OF
PARABOLA ,HENCE THE TRAJCTORY
IS PARABOLIC IN NATURE.

24. OBLIQUE PROJECTILE
 IF A BODY IS
PROJECTED
UPWARDS BY
MAKING CERTAIN
ANGLE WITH THE
HORIZONTAL IS
CALLED AS
OBLIQUE
PROJECTILE.
v

25. DESCRIPTION OF OBLIQUE
PROJECTILE
 If u be the initial velocity of the particle .
 Let ux be the initial velocity along x-axis.
 Let uy be the initial velocity along y- axis.
 Let θ be the angle with which body is projected
upwards from the horizontal.
 The x component of velocity is uniform or
constant & the y component of velocity is
accelerating motion as it is under the influence
of acceleration due to gravity.

26.  The equation of motion at any instant of
time t is given by
 Y= x tanθ – (g/2u2cosθ) x2 .
 This is the equation of parabola ,hence the
the trajectory is parabolic in nature.
CONTD…

27. TIME OF FLIGHT (T) :-
 It is the time taken by the projectile to return
to the ground or the time for which the
projectile remains in air above the
horizontal plane from the point of projection.
 It is denoted by T.
 The expression for time of flight is given by
T =( 2u sinθ)/g

28. MAXIMUM HEIGHT (H):-
 It is the greatest height to which a
projectile rises above the point of
projection. It is denoted by H.
 The expression for maximum height is
given by
H =( u2 sin2θ)/2g .
The maximum height attended by the
projectile depends upon angle of
projection.

29. HORIZONTAL RANGE(R):-
 It is the horizontal distance travelled
during the time of flight is called
horizontal range & it is denoted by R.
 The expression for range is given by
 R = (u2 sin2θ)/g
 The range will be maximum when the
value of sin2θ=1 i.e when θ =450 hence
the expression for R(max) is given by
 Rm = u2 /g

31. FREQUENTLY ASK QUESTION
1.What do you mean
by projectile?
2.What are the
examples of
projectile motion?
3.What are the different
types of projectile?
4.What do you mean
by time of flight?
5.Obtain an expression
for equation of