Question 10.5: Finding the final energies A ball of mass m and (kinetic) en...

On substituting the given data into the formula (10.15), we find that u_{1} / u_{2}=3 . It follows that

\cos \theta=\frac{\left(m_{1}-m_{2}\right) u_{2}}{2 m_{1} u_{1}},                    (10.15)

\frac{E_{1}}{E_{2}}=\frac{\frac{1}{2} m u_{1}^{2}}{\frac{1}{2}(4 m) u_{2}^{2}}=\frac{1}{4}\left(\frac{u_{1}}{u_{2}}\right)^{2}=\frac{9}{4}.

Hence E_{1}=\frac{9}{13} E \text { and } E_{2}=\frac{4}{13} E.