完全弹性碰撞的结论
$$
\begin{cases}
m_{1}v_{1}+m_{2}v_{2}=m_{1}u_{1}+m_{2}u_{2} \\
\frac{1}{2}m_{1}v^2_{1}+\frac{1}{2}m_{2}v^2_{2}
=\frac{1}{2}m_{1}u_{1}^{2}+\frac{1}{2}m_{2}u_{2}^{2}
\end{cases}
$$
$$
\begin{cases}
u_{1}= v_{c}+\frac{m_{2}(v_{2}-v_{1})}{m_{1}+m_{2}}\\
u_{2}=v_{c}+\frac{m_{1}(v_{1}-v_{2})}{m_{1}+m_{2}}
\end{cases}
$$