Answer
$\frac{K_2}{K_1} = \frac{4m_1m_2}{(m_2+m_1)^2}$
Work Step by Step
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:
$\frac{K_2}{K_1} = \frac{4m_1m_2}{(m_2+m_1)^2}$
