Relative speeds in 2D elastic collisions

Abstract When two particles undergo an elastic head-on (1D) collision, both the momentum and kinetic energy of the system of two objects are conserved (Serway and Faughn 2003 College Physics 6th edn (Pacific Grove, CA: Thomson Learning) p 168, 171, 172). It is also well-known that the two equations of conservation can be solved in elastic head-on collisions to yield the magnitude of the relative speed of approach of the two particles before the collision equals the magnitude of the relative speed of separation after the collision. In this paper, we show mathematically that for 2D elastic collisions, this relationship between the relative speeds before and after collision holds true.