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### #ActualInferiarum

Posted 16 July 2012 - 07:20 AM

To get the speed of the balls you have to work with the momenta. The sum of the momenta has to stay the same and if the collision is fully elastic also the movement energy. If the masses of all balls are the same you can just work with the velocities, i.e., the sum of all velocity vectors has to be the same before and after the collision.

edit: To be a bit more specific, lets say u1 and u2 are the velocities before the collision and n is the normalized vector from ball 1 to ball 2 at the point of collision. The velocity changes are along the direction of n, and to conserve the momenta they have to be the same, i.e.,

v1 = u1 - a*n
v2 = u2 + a*n

for an elastic collision the parameter a can be calculated with the conservation of the energies. The result I calculated is

a = <u1 - u2,n>

where < . ,. > denotes the inner product. That is, the total change in velocity a*n is the projection of the difference u1 - u2 onto the 'line of collision'

### #1Inferiarum

Posted 16 July 2012 - 03:49 AM

To get the speed of the balls you have to work with the momenta. The sum of the momenta has to stay the same and if the collision is fully elastic also the movement energy. If the masses of all balls are the same you can just work with the velocities, i.e., the sum of all velocity vectors has to be the same before and after the collision.

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