Physics of Projectile Motion

Exploding fireworks follow a parabolic trajectory.

What’s wrong with this picture ?

Answer: It never happens ! Only whenthere 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 Motionalong y-yaxis and Uniform Motion along x-axis.

1. Along x, the projectile travels with constant velocity. vx=vxo x = vxot

2. 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.

Projectile Motion = Sum of 2 Independent Motions

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

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)

x

yuniform motion

verticalmotion

Projectilemotion

Launch speed = Return Speed. Speed is minimum at apex of parabolic trajectory.

Horizonal component

Net velocity

vx

vertical component

vy v

Above: Vectors areadded in geometricFashion.

Velocity Components at various points of the 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 componentAnswer: 45°

Everyday Examples of Projectile Motion

1.Baseball being thrown2.Water fountains3.Fireworks Displays4.Soccer ball being kicked5.Ballistics Testing