How do you work out from conservation of momentum how momentum is distributed?

Question

For example, if two balls of different mass travelling at different speeds strike each other from opposite directions, I know due to conservation of momentum that the total momentum after the collision will be the same, and that both balls will now be moving away from each other, and their masses will be the same- but how do you work what their individual velocites will be? How is the total final momentum distributed between them?

Answer 1

Each ball will leave the collision at the same velocity it entered.

Answer 2

Two balls: M1, M2 at speeds V1 and U1, collide resulting in new velocities V2 and U2
Initial momentum= M1V1+M2U1
Collision occurs, final momentum=M1V2+M2U2

M1V1+M2U1=M1V2+M2U2

There exists a value e such that V1-U1 = -e(V2-U2)
(If e is 1 the balls are perfectly elastic, if e=0 they have no elasticity and hence are like clay or something like that.)

Assuming e=1 as you have not given it in your question, the velocities of the balls relative to each other will have equal magnitude and opposite direction to before the collision.

V1-U1=U2-V2

You now have 2 equations and 4 unknowns, so to work out each velocity you need to be given at least 2 unknowns in the question.

Answer 3

Peter's analysis is right. But I'd like to comment on one of his paragraphs in order to disagree with psycho_je....

Peter said
"Assuming e=1 as you have not given it in your question, the velocities of the balls relative to each other will have equal magnitude and opposite direction to before the collision.

V1-U1=U2-V2"

That means both balls have equal change in velocity. You probalby have seen one billiard ball (ball1) hit a stationary ball (ball2). Ball1 stops (or nearly so - the rotation the ball had affects this) and ball2 takes of with nearly the same velocity ball1 had.