1. HASMUKH GOSWAMI COLLEGE OF ENGINEERING, VAHELAL
PRESENTATION ON
Motion in 2 dimensions
PREPARED BY :-
DOSHI AKASH KAMLESHBHAI

2. 1) Displacement, velocity and acceleration
displacement is the vector from initial to final position

3. 1) Displacement, velocity and acceleration
average velocity

4. 1) Displacement, velocity and acceleration
instantaneous velocity
v is tangent to the path
v can change even if v is constant

5. 1) Displacement, velocity and acceleration
average acceleration
not in general parallel
to velocity

6. 1) Displacement, velocity and acceleration
instantaneous acceleration

7. 1) Displacement, velocity and acceleration
instantaneous acceleration
- object speeding up in a straight line
acceleration parallel to velocity
- object at constant speed but changing direction
acceleration perp. to velocity

8. 2) Equations of kinematics in 2d
Superposition (Galileo): If an object is subjected to two separate influences, each producing a characteristic type of motion, it responds to each without modifying its response to the other.
That is, we consider x and y motion separately

9. 2) Equations of kinematics in 2dvy vx vx vy
A bullet fired vertically in a car moving with constant
velocity, in the absence of air resistance (and ignoring
Coriolis forces and the curvature of the earth), will fall
back into the barrel of the gun. That is, the bullet’s
x-velocity is not affected by the acceleration in the
y-direction.

10. 2) Equations of kinematics in 2d
That is, we can consider x and y motion separately

11. 2) Equations of kinematics in 2d
That is, we can consider x and y motion separately

12. Example y x

13. 3) Projectile Motion (no friction)
Equations
Consider horizontal (x) and vertical (y) motion separately (but with the same time)
Horizontal motion: No acceleration ==> ax=0
Vertical motion: Acceleration due to gravity ==> ay= ±g
- usual equations for constant acceleration

14. 3) Projectile Motion (no friction)
Example: Falling care package
Find x.
Step 1: Find t from
vertical motion
Step 2: Find x from
horizontal motion x

15. 3) Projectile Motion (no friction)
Example: Falling care package
Step 1:
Given ay, y, v0y x

16. 3) Projectile Motion (no friction)
Example: Falling care package
Step 2: x

17. 3) Projectile Motion (no friction)
b) Nature of the motion: What is y(x)?
Eliminate t from y(t) and x(t): x y
y(x) is a parabola

18. 3) Projectile Motion (no friction)
c) Cannonball physics
Find (i) height, (ii) time-of-flight, (iii) range

19. 3) Projectile Motion (no friction)
c) Cannonball physics
Height:
Consider only y-motion: v0y given, ay=-g known
Third quantity from condition for max height: vy=0

20. 3) Projectile Motion (no friction)
c) Cannonball physics
(ii) Time-of-flight:
Consider only y-motion: v0y given, ay=-g known
Third quantity from condition for end of flight; y=0

21. 3) Projectile Motion (no friction)
c) Cannonball physics
(iii) Range:
Consider x-motion using time-of-flight: x=v0xt