I'm stuck, please help?

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 98 miles per hour (vball = 43.1 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 = 61024 kg)?


(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.


I think i could figure this out if I knew how to write up the energy principle equation. Either way, can someone please explain how to do this? I just wanna get this done (but also how i can do it of course)

Thanks everyone

Alright figured it out!

set it up as

p1+p2=p3+p4

p1 = initial momentum of ball
p2 = 0 (this is the wall)
p3 = initial momentum of ball, times 2 since it rebounds
p4 = solve for this to find rebound momentum of earth
These are all interchangeable with deltaK for energy changes, solved same way

Thanks for the suggestion on using conservation of momentum

Answer 1

USE PRINCIPLE OF CONSERVATION OF linear MOMENTUM.

earth gas lower KE because it has huge mass and huge inertia

Answer 2

Conservation of momentum