Chapter 3

1. Chapter3 Motion in 2 dimensions

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 v is tangent to the path v can change even if v is constant • instantaneous velocity

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 2d vy 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) x Example: Falling care package Find x. Step 1: Find t from vertical motion Step 2: Find x from horizontal motion

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

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

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