Elastic headon collision, consider two particles one is moving and another one is stationary with their respective masses m and M/m

Question

Elastic headon collision, consider two particles one is moving and another one is stationary with their respective masses m and \(\frac{M}{m}\) . A moving particle meets collides elastically on stationary particle in the opposite direction. Find the kinetic energy of the stationary particle after a collision?

Answer 1

mass of the moving particle m₁ = m (say) 

mass of the stationary particle m₁ = \(\frac{1}{m}\) M 

Velocity of the moving particle before collision =v_1i (say) 

Velocity of the stationary particle before collision = v_2i = 0 

Velocity of the stationary particle after collision = v_2f (say)

Kinetic energy of the stationary particle after a collision

= \(\frac{4m}{(1+ m^2)}\) x kinetic energy of moving particle before collision