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I was thinking about colliding balls and the conservation of momentum.

If a ball weighing 10kg travelling at 10m/s collides with another stationary ball weighing 5kg, then the two balls should be moving with some velocity so that the overall momentum is 100kg m/s

My question is what govern's the distribution of the momentum between the two balls?

The 10kg ball coming to a complete stop after the collision and the 5kg ball being shot off at 20m/s is a valid configuration after the collision. but there are an infinite number of valid configurations possible.

How does one determine exactly what will happen? what else do we need to consider to accurately predict the momentum of each ball after the collision?