Question

A ball of mass 0.5 kg makes a head-on elastic collision with a second ball (at rest) and rebounds with a speed equal to 0.450 its original speed. The mass of the second ball in kg

Answer 1

Since in elastic collision there is no loss of energy

therefore we can apply conservation of momentum on the system of two balls

Let initial velocity of ball 1 be 'v' and it is given that second ball is at the rest initially

therefore initial momentum of system before the collision , p_initial = 0.5 * v

now let after the collision the velocity of ball 1 be 'v1' and velocity of ball 2 be 'v2' and let mass of ball 2 be 'm2'.

and v1 = (-0.45)*v , negative sign is due to direction of velocity of ball 1 after collision

final momentum of system , p_final = m2*v2 + 0.5*v1 = m2*v2 - 0.225*v

equalizing both  p_initial =  p_final

0.5*v = m2*v2 - 0.225*v

0.725*v = m2*v2

Also applying initial kinetic energy of system = final kinetic energy of system

[1/2]*m1*[v]² = [1/2]*m1*[v1]² +    [1/2]*m2*[v2]²

putting m1 = 0.5 kg and using 0.725*v = m2*v2

we get on solving m2 = 1.31818 kg.