How will the speeds be distributed after the collision?

Question

Physics

There are two balls, having different speeds and masses, flying towards each other at some angle. How will the velocity vectors of the balls change after the collision?

Answer 1

1. Law of conservation of momentum. The sum of the momenta of the balls (vector quantity) is conserved.
2. The exchange of energy (and hence impulses) occurs strictly along the normal at the point of impact.
Yes, and I see no reason to retell in detail, the article will tell better: https://ru.wikipedia.org/wiki/Impact#Absolutely_elastic...

Answer 2

The answer will depend heavily on the impact model.
For specific calculations, it is better to go to the ISO associated, for example, with the center of the second ball before the collision and direct the X axis in it parallel to the velocity of the first ball. Then the minimum set of parameters of this system: the masses of the balls, the speed of the incident ball and the impact distance (between the lines parallel to the X axis, passing through the centers of the balls).
So, with absolutely elastic collision and neglecting the twisting of the balls, momentum, energy and angular momentum are conserved. You can write down the corresponding equations, they are enough to determine the final velocities (in this case, the law of conservation of momentum requires that the projection of the velocity of the incident ball onto the tangent plane at the point of impact does not change after the impact - the same conclusion can be reached if we assume that there are no friction).
Such a model, of course, will have little in common with reality. In reality, friction at the point of impact is a significant factor (remember hits in curl billiards). This friction causes a deviation from the law of conservation of energy and spins the balls. The physics of the collision will be quite complex and the specific answer will depend on the nature of the deformation and the resulting elastic forces and their relationship with the forces of friction.
Even with a central impact (forehead to forehead, impact parameter = 0, no spinning of the balls, friction forces do not matter), everything is not easy. The law of conservation of energy may not be fulfilled even in the case of an elastic material of the balls. In this good bookstarting from page 101, collisions of long elastic rods are considered. If the lengths (and material) of the rods are the same, the result is the same as in a school textbook (the rods exchange speeds). When one of the rods is longer, the macroscopic law of conservation of energy "ceases" to be fulfilled, because part of the kinetic energy after the collision remains in the longer rod in the form of elastic waves.
I think you are only required to consider the first case.