Solution
= Solution
With $\gamma=(1-v^2/c^2)^{-1/2}$, <four-momentum conservation> gives total <energy> $E=(\gamma m_1+m_2)c^2$ and <momentum> $\mathbf p=\gamma m_1\mathbf v$. The compound system therefore has
$$
\boxed{M=\sqrt{m_1^2+m_2^2+2\gamma m_1m_2},\qquad
\mathbf V=\frac{\gamma m_1}{\gamma m_1+m_2}\mathbf v}.
$$
Here $M^2c^4=E^2-c^2p^2$. The excess over $m_1+m_2$ is retained <internal energy>, assuming <absorption> without escaping <radiation>.