<P> and dependent equation, the sum of above equations: </P> <Dl> <Dd> m 1 e s 1 + m 2 e s 2 = m 1 e s 3 + m 2 e s 4 (\ displaystyle m_ (1) e ^ (s_ (1)) + m_ (2) e ^ (s_ (2)) = m_ (1) e ^ (s_ (3)) + m_ (2) e ^ (s_ (4))) </Dd> </Dl> <Dd> m 1 e s 1 + m 2 e s 2 = m 1 e s 3 + m 2 e s 4 (\ displaystyle m_ (1) e ^ (s_ (1)) + m_ (2) e ^ (s_ (2)) = m_ (1) e ^ (s_ (3)) + m_ (2) e ^ (s_ (4))) </Dd> <P> subtract squares both sides equations "momentum" from "energy" and use the identity cosh 2 (s) − sinh 2 (s) = 1 (\ displaystyle (\ mbox (cosh)) ^ (2) (s) - (\ mbox (sinh)) ^ (2) (s) = 1), after simplicity we get: </P>

Discuss the elastic collision of two bodies in one dimension