Projectile Motion

1. Projectile Motion

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/s2 for gravity. • Trajectory – path of a projectile

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

5. Horizontally launched cannonball

6. Non-horizontally launched cannonball

7. Vertical Component • Distance • x = Vit + ½ gt2 *Vi is 0, so it cancels! • x = ½ gt2 • Velocity • Vf = Vi + gt *Vi is 0, so it cancels! • V = gt

8. Horizontal Component • Distance • x = Vt • Velocity • V = d/t

9. 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? • x = ½ gt2 • 44 = ½ (9.80)(t2) • 44 = 4.90( t2) • 8.9796 = t2 • t = 3.0 s 15m/s 44m

10. 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? • x = Vt • x= (15)(3.0) • x = 45 m d

11. 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

12. 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? • x= ½ gt2 • x = ½ (9.80)(2.32) • x = 25.92 m

13. 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? • x= Vt • x = (18)(4.6) • x = 82.8 m

14. 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