# Elastic collisons in space

Two balls Y and Z collide elastically in space. If Z is initially at rest how would you choose it's mass in relation to Y so that it would recoil with the greatest (1) KE (2) Momentum

Kinetic Energy: KE = (1/2)mv^2

Momentum: P = mv

Would you have to have a smaller mass for Z so that it would recoil with greater KE than Y?

And for momentum would you have to have a larger mass for Z so it would recoil with greatre momentum?

How do you explain them in terms of the equations? I think I understand the momentum....if you plug in larger mass than you have a larger P...but KE I'm not sure? Wouldn't you also have a larger KE if you plugged in larger mass? If Z was really large it wouldn't move it all so I would think it would have to be small would it not?

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Anyone have input for this?

Momentum is always conserved for all cases so the ball or block that is going to hit the one that is resting has a constant value of momentum;

as you can see from the equaiton p=m.v the value of the momentum is about the values of the blocks or balls mass and velocity.

So to get the max value of kinetic energy i would take m as a small value because the degree of it is 1, if you double your velocity your kinetic energy would increase as a factor of 4.

(Kinetic energy of a block is 1/2mv2 as you mentioned )