1. Chapter 3 Motion in two or more dimensions

2. Two dimensional motion

3. Vector Notation

4. Example

6. The vertical and horizontal components decouple

7. Vertical and horizontal decouple

8. 1D equation splits into 2D Similarly for the velocity:

9. Free Fall (Projectile Motion)

10. Quiz 1-2 Feb 21

11. The General Picture

12. A batted baseball A baseball flies at speed v 0 =37m/s at an angle of α 0 =53.1°. Find: a)The position, velocity (magnitude and direction) of the ball at t=2s. b)The time when the ball reaches the highest point and the height at that point. c)The horizontal range (the horizontal distance form the starting point to where the ball hits the ground).

13. First find the initial velocity v 0x, v 0y. v 0x v 0y

14. Velocity (magnitude and direction)

15. The highest point

16. Horizontal range To find the horizontal range, we have to first figure out when the ball hits the ground.

17. Different initial and final heights You toss a ball from your window 8m above the ground. The ball leaves your hand at 10m/s at an angle of 20° below the horizontal. How far horizontally will it hit the ground?

18. First find the initial velocity v 0x, v 0y. v 0x v 0y

19. Find the time it hits the ground

20. Find the horizontal distance

21. Circular motion

22. Acceleration of Circular Motion

23. Centripetal acceleration r v x y (x,y) speedvelocityEven though the speed of the object is constant, the velocity is constantly changing because of the changing direction. That is why the acceleration is non-zero.

24. Must remember this: Using this you can convert freely among ω, T, f and v.

25. Centripetal force and acceleration

26. Uniform Circular Motion A fighter pilot flying in a circular turn will pass out if the centripetal acceleration he experiences is more than about 9 times the acceleration of gravity g. If his F18 is moving with a speed of 300 m/s, what is the approximate diameter of the tightest turn this pilot can make and survive to tell about it ? (a) 500 m (b) 1000 m (c) 2000 m

27. Solution 2km

28. Horizontal and Vertical Range