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

Explanation

mass of the moving particle `m_(1)` = m (say)
mass of the stationary particle `m_(2) = 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)
`v_(2f) = (m_(2)-m_(1))/(m_(1)+m_(2)) v_(2i) + (2m_(1))/(m_(1)+m_(2)) v_(1i) ("or") v_(2f) = 0 + (2M)/(m+M/m) v_(1i) = (2m)/(m+1) v_(1i)`
kinetic energy of the stationary particle after a collision
`=1/2 M/m ((2m)/(m+1) v_(1i))^(2) = (4m)/((1+m)^(2)) xx 1/2 M v_(1i)^(2)`
`= (4m)/((1+m)^(2)) xx` kinetic energy of moving particle before collision