Question

A ball of mass m makes a head-on elastic collision with a second ball (at rest) and rebounds with a speed equal to one-fourth its original speed. What is the mass of the second ball?

Answer 1

$$p_i=p_f\\mv=-\frac{1}{4}mv+MV\\MV=\frac{5}{4}mv$$

$$0.5mv^2=0.5m(0.25)^2v^2+0.5MV^2\\ 0.5mv^2=0.5m(0.25)^2v^2+0.5(1.25)^2\frac{m^2}{M}v^2\\ M=0.6m$$