Proof That Relative Speed is Conserved in Elastic Collisions
Kinetic energy is conserved in elasic collisions, and momentum is always conserved. To prove that relative speed is conserved suppose that masses
have initial velocities
final velocities
so initial speeds
and final speeds
a
Then conservation of kinetic energy implies
(1)
Conservation of momentum implies
(2)
From (1)
(3)
From (2)
Hence
Then
and relative speed is conserved.
