We can use the textbook results for head-on elastic collisions to analyze the re

Question

We can use the textbook results for head-on elastic collisions to analyze the recoil of the Earth when a ball bounces off a wall embedded in the Earth. Suppose a professional baseball pitcher hurls a baseball (m = 155 grams = 0.155 kg) with a speed of 100 miles per hour (vball = 44.0 m/s) at a wall, and the ball bounces back with little loss of kinetic energy.

(b) Calculate the recoil kinetic energy of the Earth

(c) Calculate the kinetic energy of the baseball

The Earth gets lots of momentum (twice the momentum of the baseball) but very little kinetic energy.

Explanation / Answer

ball recoils with little loss of Ke that means ball recoil with same speed in opposite direction.

using momentum conservation for ball-earth system:

initial = final momentum of system

0.1555 x 44 + (6 x 10^25 x 0 ) = (0.155 x -44 ) + (6 x 10^25 x v)

v = 2.273 x 10^-25 m/s ......Ans(a)

b) KE = m v^2 /2 = (6 x 10^25 ) ( 2.273 x 10^-25)^2 /2

      = 1.55 x 10^-24 J

c) KE of ball = 0.155 x 44^2 /2 = 150.04 J

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