התנגשות עם מקדם תקומה

\varepsilon=-\frac{u_{1}-u_{2}}{v_{1}-v_{2}}=-\frac{u'_{1}-u'_{2}}{v'_{1}-v'_{2}}

\varepsilon=-\frac{u'_{1}-\frac{m_{1}}{m_{2}}u'_{1}}{v'_{1}-\frac{m_{1}}{m_{2}}v'_{1}}=-\frac{u'_{1}}{v'_{1}}\Rightarrow u'_{1}=-\varepsilon v'_{1}

u_{1}=u'_{1}+v_{cm}=-\varepsilon v'_{1}+v_{cm}=-\varepsilon v_{1}+\left(1+\varepsilon\right)v_{cm}

u_{1}=-\varepsilon v_{1}+\left(1+\varepsilon\right)\cdot\frac{m_{1}v_{1}+m_{2}v_{2}}{m_{1}+m_{2}}=v_{1}\cdot\frac{m_{1}-\varepsilon m_{2}}{m_{1}+m_{2}}+v_{2}\cdot\frac{\left(1+\varepsilon\right)m_{2}}{m_{1}+m_{2}}

u_{2}=v_{2}\cdot\frac{m_{2}-\varepsilon m_{1}}{m_{1}+m_{2}}+v_{1}\cdot\frac{\left(1+\varepsilon\right)m_{1}}{m_{1}+m_{2}}