Physics of Projectile Motion

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Presentation transcript:

Physics of Projectile Motion Exploding fireworks follow a parabolic trajectory.

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

Why do projectiles fly in a parabola?

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.

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.

What’s the similarity between a freely-falling ball and a projectile ? 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)

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

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°

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