Projectile Motion

1. Projectile Motion Notes

2. Projectile Motion • Definition • Movement in 2 dimensions rather than 1 • 2 models • Horizontal launch • Kicking a stone off a bridge • Angled launch • Golf/base/football • Artillery shell • In both models, the only effect on the projectile, after leaving the launch, is g↓

3. Horizontal Launch • Basic premise • In the absence of air resistance… • The objects are in free fall! • Both objects reach the ground at the same time

4. vx dy dx Horizontal Launch • Analysis technique • Break the model down into vertical (y) and horizontal (x) component columns • Vertical (y) ↓ • vo = 0 (drop model) • g = 9.8 (always on Earth!) • dy = height • t = time to fall • Horizontal (x) → • dx = range • vx = initial velocity in horizontal direction • t = time to fall

5. vx dy dx Projectile Motion Identify the target parameter, and start in the opposite column. ex. If vx (horizontal column) is requested, start solving in the vertical column Use the time (t) value as common to both axes – the time taken to follow the parabolic path is the same as a simple drop!

6. vx dy dx Ex. Horizontal • A baseball rolls off a 0.7 m high desk and strikes the floor 0.25 m away from the base of the desk. • How fast was it rolling?

7. vx dy dx Solution • 1) vertical • dy = vot + ½ g t2 • 0.7= 0 + ½ (9.8) t2 • t = 0.38 seconds (use in the “other” column) • 2) horizontal • dx = vx*t • 0.25 = vx* 0.38 • vx = 0.66 m/s

8. Practice • Your turn!

9. What if the projectile is launched at an angle to the horizontal?

10. Angled Launch Projectile Motion • Definition • The motion of the projectile is uniquely defined by: • Its launch angle (Ө) and • its initial velocity (vo)

11. Angled Launch Parameters

12. Angled Launch

13. Angled Launch – refer to sheet • Max Height: • dymax= (V0 sin )2/2g • Range: • d xmax= V02 sin (2) / g • Time to max height: • t = (V0 sin)/g • Total time in air (hang time) • (time up=time down) • ttotal = 2 (V0 sin)/g

14. Comparing Trajectories Max range angle Which angle provides the maximum down range (x) distance?

15. Practice time • Your turn!