## Essential University Physics: Volume 1 (4th Edition)

$\frac{K_2}{K_1} = \frac{4m_1m_2}{(m_2+m_1)^2}$
We know the following equations for each kinetic energy: $K_1 = \frac{1}{2}m_1v_1^2$ $K_2 = \frac{1}{2}m_2v_2^2 = \frac{2m_1^2v_1^2m_2}{(m_2+m_1)^2}$ Thus, it follows: $\frac{K_2}{K_1} = \frac{4m_1m_2}{(m_2+m_1)^2}$