Page "Momentum" Paragraph 50

A change of reference frame can often simplify the analysis of a collision.

For example, suppose there are two bodies of equal mass, one stationary and one approaching the other at a speed ( as in the figure ).

The center of mass is moving at speed and both bodies are moving towards it at speed.

Because of the symmetry, after the collision both must be moving away from the center of mass at the same speed.

Adding the speed of the center of mass to both, we find that the body that was moving is now stopped and the other is moving away at speed.

The bodies have exchanged their velocities.

Regardless of the velocities of the bodies, a switch to the center of mass frame leads us to the same conclusion.

Therefore, the final velocities are given by