1. Day 15, Wednesday, 16 September, 2015 2 D Motion 2 D Motion Chapter 3 Motions in different directions Royal Gorge problem Tennis Serve Problem Frames of Reference

2. Photo of a meteor shot from the International Space Station.

3. The Constant Acceleration of Gravity (at the Earth’s surface) g = 9.8 m/s 2

4. Constant Velocity d = d 0 + v t position with constant velocity

5. Changing Velocity (with acceleration) d = d 0 + ½ (v + v 0 )t final position with changing velocity

6. Constant Acceleration d = d 0 + v 0 t + ½ a t 2 Distance with constant acceleration v = v 0 + a t velocity with constant acceleration v 2 = v 0 2 + 2 a (d – d 0 ) final velocity with constant acceleration

7. What happens in Vegas stays in Vegas

8. What happens in Y Stays in Y

9. Vertical and Horizontal motion both contribute to the overall trajectory, but do not affect each other.

10. Independence of Motion in Multiple Dimensions d = d 0 + v 0 t + 1/2at 2 y axis (vertical) d = d 0 + v 0 tx axis (horizontal)

11. Projectiles launched at an angle Two Solutions (there is a square in the motion equations ) One maximum range(45°)

12. Effects of Air resistance

13. Problems 1. The Royal Gorge bridge in Colorado rises 321 m above the Arkansas river. Suppose you kick a rock horizontally off the bridge. The magnitude of the rock’s horizontal displacement is 45.0 m. Find the speed at which the rock was kicked.

14. Rock kicked off the bridge Givens:y = -321 m x = 45.0 m ay = g = -9.81 m/s 2 Unknown:V i = V x = ?

15. Tennis Serve At serve, a tennis player hits the ball horizontally. 1. What minimum speed is required for the ball to clear the 0.90-m-high net about 15.0 m from the server if the ball is “launched” from a height of 2.50 m? 2. How long will it be in the air? 3. Where will the ball land if it just clears the net? 4. Will it be “good” in the sense that it lands within 7.0 m of the net?

17. Frames of Reference

18. Credits Upper and Lower trajectories www.troubleshooters.com/tpromag/20020 7/200207.htm www.troubleshooters.com/tpromag/20020 7/200207.htm Photo of meteor : Daily Mail

19. Credits II Horizontal and vertical components graph www.physclips.unsw.edu.au/jw/projectiles. htm www.physclips.unsw.edu.au/jw/projectiles. htm Air resistance on a projectile www.viswiki.com/en/Trajectory_of_a_proje ctile www.viswiki.com/en/Trajectory_of_a_proje ctile