In an American football game, an 80 Kg receiver jumps straight in the air and ca

Question

In an American football game, an 80 Kg receiver jumps straight in the air and catches a 0.5 Kg football thrown towards him. Just before the catch, the receiver is a height 0.5m off of the ground. And the football is traveling horizontally at a speed of 40 m/s (90 mph). Assuming the catch is a perfectly inelastic collision (the ball and the player move together afterwards): how fast are the ball and player moving immediately after the catch? what is the total kinetic energy immediately after the catch? how much energy was lost during collision?

Explanation / Answer

here,

mass of football player , m1 = 80 kg

mass of football , m2 = 0.5 kg

u = 40 m/s

1)

let their final speed be v

using conservation of momentum

m2 * u = (m1 + m2) * v

0.5 * 40 = ( 80 + 0.5) * v

solving for v

v = 0.25 m/s

the final speed is 0.25 m/s

2)

the total kinetic energy , KE = 0.5 * (m1 + m2) * v^2

KE = 0.5 * ( 80 + 0.5) * 0.25^2

KE = 2.52 J

3)

the energy lost in the collision , dKE = 0.5 * m2 * u^2 - KE

dKE = 0.5 * 0.5 * 40^2 - 2.52

dKE = 397.48 J

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