Mv = Mv_{1} + mv_{2}

\frac{1}{2}Mv^{2} = \frac{1}{2}Mv_{1}^{2} + \frac{1}{2}mv_{2}^{2}

\begin{aligned}v_{1} & = [1 − \frac{2}{1 + (M/m)}] v \\ v_{2} & = [\frac{2}{1 + (m/M)}] v \end{aligned}

\begin{aligned}v_{1} & ≃ (1 − \frac{2m}{M}) v ∼ v \\ v_{2} & ≃ 2v \end{aligned}