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-fifth its original speed. What is the mass of the second ball?

initial momentum
= mu + M *0
= mu

final momentum
= - 0.2 mu + M v
conservation of momentum
mu = - 0.2 mu + M v
1.2 mu = Mv
v = 1.2 mu/ M

conservation of energy
0.5 mu^2 + 0.5 M *0^2 = 0.5* m(0.2u)^2 + 0.5M v^2
mu^2 = m(0.2u)^2 + M v^2
m u^2 = 0.04 mu^2 + M [1.2 mu/ M]^2
0.96 mu^2 = 1.44 m^2u^2 / M
0.96 = 1.44 m / M
M = 1.5 m
answer