Explanation

(a) If after the collision of two bodies, the total kinetic energy of the bodies remains the same as it was before the collision, and also momentum remains same, then it is a case of perfectly elastic collision.
Momentum before collision= Momentum after collision
Kinetic energy before collision
=Kinetic energy after collision
Also,${\ u}_{1} - u_{2} = - \left( v_{1} - v_{2} \right)$
Where ($\ u_{1} - u_{2}$) is the relative velocity before the collision and $(v_{1} - v_{2})$is the relative velocity after the collision. Thus, in a perfectly elastic collision the relative velocity remains unchanged in magnitude, but is reserved in direction. Hence, velocity of the last ball is $- 0.4\ ms^{- 1}$.