1. 1 Projectile Motion

2. 2 Projectile An object that moves through the air only under the influence of gravity after an initial thrust For simplicity, we’ll use 9.8 m/s 2 for gravity. Trajectory – path of a projectile

3. 3 The vertical and horizontal components of a projectile are independent of each other If 1 ball were dropped and another ball launched forward from the same height, they would hit the ground at the same time.

4. Video Break Mythbusters 4

5. 5 Force vectors for projectiles Draw both horizontal and vertical vectors

6. Vertical Horizontal d = ½ gt 2 V = gt d = Vt V = d/t

7. 7 Horizontally launched cannonball

8. 8 Non-horizontally launched cannonball

9. 9 Vertical Component Distance d = V i t + ½ gt 2 *V i is 0, so it cancels! d = ½ gt 2 Velocity V f = V i + gt *V i is 0, so it cancels! V = gt

10. 10 Horizontal Component Distance d = Vt Velocity V = d/t

11. 11 Example) A stone is thrown horizontally at 15 m/s from the top of a cliff 44 m high. a) How long does it take to fall? d = ½ gt 2 44 = ½ (9.80)(t 2 ) 44 = 4.90( t 2 ) 8.9796 = t 2 t = 3.0 s 44m 15m/s

12. 12 Example) A stone is thrown horizontally at 15 m/s from the top of a cliff 44 m high. b) How far from the base of the cliff does it land? d = Vt d = (15)(3.0) d = 45 m d

13. 13 Example) A stone is thrown horizontally at 15 m/s from the top of a cliff 44 m high. c) What is its vertical speed when it hits the ground? V = gt V = (9.80)(3.0) V = 29.4 m/s

14. 14 Example 2) A ball is thrown at a horizontal speed of 18 m/s. It’s flight time is 4.6 seconds. How high does the ball go? d = ½ gt 2 d = ½ (9.80)(2.3 2 ) d = 25.92 m

15. 15 Example 2) A ball is thrown at a speed of 18 m/s. It rises and falls in 4.6 seconds. How far away does it land? d = Vt d = (18)(4.6) d = 82.8 m

16. 16 Example 2) A ball is thrown at a speed of 18 m/s. It rises and falls in 4.6 seconds. What is its vertical speed when it hits the ground? V = gt V = (9.8)(2.3) V = 22.54 m/s