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 masseshave initial velocitiesfinal velocitiesso initial speedsand final speedsa
Then conservation of kinetic energy implies
Conservation of momentum implies (2)
From (1) (3)
Thenand relative speed is conserved.