## Essential University Physics: Volume 1 (3rd Edition)

$v_{1f}=\frac{m_1-m_2}{m_1+m_2}v_{1i}+\frac{2m_2}{m_1+m_2}v_{2i}$
We know the following equations from conservation of momentum and conservation of kinetic energy: $\frac{1}{2}mv_{1i}^2+\frac{1}{2}mv_{2i}^2=\frac{1}{2}mv_{1f}^2+\frac{1}{2}mv_{2f}^2$ $m_{1}v_{1i}+m_2v_{2i}=m_{1}v_{1f}+m_2v_{2f}$ Using substitution and combining these equations gives: $v_{1f}=\frac{m_1-m_2}{m_1+m_2}v_{1i}+\frac{2m_2}{m_1+m_2}v_{2i}$