Where a Ball Ends Up after a Collision If a moving ball collides
with a stationary one, then the moving ball should be replaced
along its original trajectory at the point corresponding to the
sum of the distances travelled by both balls from the point of
collision. The above result incorporates the assumptions that
there is a constant deceleration of the ball1, the collision is
elastic (energy is conserved) and the balls have the same
weight. A simple proof of why the distance travelled by a ball
is proportional to its energy is given in the Appendix. Under
those conditions the distance travelled by a ball is directly
proportional to the energy it carries. This is reassuring – hit
the ball with twice the energy and it goes twice as far. When
the balls collide the energy is shared between them and they
each move a distance corresponding to the fraction of the energy
they received. Add the distances travelled by the separate balls
and it gives you the distance which would have been travelled by
the unhindered b