A brother and sister are standing next to each other at rest on a surface of frictionless ice. The brother’s mass is exactly twice that of his sister’s. The sister suddenly pushes her brother. As a result, the sister moves with kinetic energy K. What is the resulting kinetic energy of the brother?

Question

A brother and sister are standing next to each other at rest on a surface of frictionless ice. The brother’s mass is exactly twice that of  his sister’s. The sister suddenly pushes her brother. As a result, the  sister moves with kinetic energy K. What is the resulting kinetic energy of the brother?

i know the answer is K/2 but i don't know why. Can someone explain it to me please?

Max Anderson · Accepted Answer

Ok so I struggled with this too, but I think I just figured out how to do it.
You can think of this problem as an elastic collision(hopefully) where Ke is conserved and momentum is conserved. I'm not going to bring momentum into this, but. Kbrother = Ksister

Ksister = 1/2 * M * V^2
Kbrother = 1/2 * 2M * V^2

We can break this down into
Kbrother = 2 * (1/2MV^2)
Ksister = (1/2MV^2)
Kbrother = 2 * (Ksister)
Kbrother/2 = Ksister

so that's how I did it and thought about it. I don't know if that's the right way to do it though.