Physics of Projectile Motion

1. Physics of Projectile Motion Exploding fireworks follow a parabolic trajectory.

2. What’s wrong with this picture ? Answer: It never happens ! Only when there is no gravity.

3. Why do projectiles fly in a parabola?

4. A History of Projectile Motion Aristotle: The canon ball travels in a straight line until it lost its ‘impetus’. Galileo: - a result of Free Fall Motion along y-yaxis and Uniform Motion along x-axis.

5. Projectile Motion = Sum of 2 Independent Motions • 1. Along x, the projectile travels with constant velocity. • vx=vxo x = vxot • Along y, the projectile travels in free-fall fashion. • vy = vyo – gt y = vyot – (1/2) gt2 , g= 9.8 m/s2 • Projectile motion = a combination of uniform motion along x and • uniformly accelerated motion (free fall) along y.

6. What’s the similarity between a freely-falling ball and a projectile ? y uniform motion Projectile motion vertical motion x A dropped ball falls in the same time as a ball shot horizontally. Along the vertical, their motions are identical (uniformly accelerated motion (free-fall). Along the horizontal, notice the ball fired horizontally covers the Same distance in the same unit time intervals (uniform motion along x)

7. vertical component v vy  Velocity Components at various points of the Trajectory Net velocity vx Horizonal component Above: Vectors are added in geometric Fashion. Launch speed = Return Speed. Speed is minimum at apex of parabolic trajectory.

8. At what angle do I launch for Maximum Range ? Need to stay in air for the longest time, and with the fastest horizontal velocity component Answer: 45°

9. Everyday Examples of Projectile Motion • Baseball being thrown • Water fountains • Fireworks Displays • Soccer ball being kicked • Ballistics Testing