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 96 miles per hour (vball = 42.2 m/s) at a wall, and the ball bounces back with little loss of kinetic energy. (a) What is the recoil speed of the Earth (M = 6*10^24 kg)? vEarth = Incorrect: Your answer is incorrect. m/s (b) Calculate the recoil kinetic energy of the Earth and compare to the kinetic energy of the baseball. The Earth gets lots of momentum (twice the momentum of the baseball) but very little kinetic energy. KEarth = J Kbaseball = J

Explanation / Answer

a)

conserving momentum

0.155 x42.2 = 0.155 x(-42.2 ) + MVearth

Vearth = 2.18 x 10 ^-24 m/sec

b)

Kbaseball = 0.5x0.155x42.2x42.2 = 138.0151 J

Kearth = 0.5 x M x Veart^2 = 1.426 x 10^-23 J

since KE is equal to P^2/2M

whaere P is momentum

eventhough earth gets double momentum but the mass of earth is very large so it gets less KE

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