Two spheres A and B moving in opposite directions have velocities of 10ms^-1 and 20ms^-1. The two spheres collide with each other elastically. If A continues to move in the same direction at 4 ms^-1, the velocity of sphere B just after the collision is

Given,

${\mathrm{u}}_{\mathrm{A}}=10\mathrm{m}/\mathrm{s}, {\mathrm{u}}_{\mathrm{B}}=-20\mathrm{m}/\mathrm{s}, {\mathrm{v}}_{\mathrm{A}}=4\mathrm{m}/\mathrm{s}, {\mathrm{v}}_{\mathrm{B}}=?$

The coefficient of restitution is unity because the collision is elastic.

$\mathrm{e}=\frac{{\mathrm{v}}_{\mathrm{B}}-{\mathrm{v}}_{\mathrm{A}}}{{\mathrm{u}}_{\mathrm{A}}-{\mathrm{u}}_{\mathrm{B}}}=1$

$$\begin{gathered} {\mathrm{v}}_{\mathrm{B}}-{\mathrm{v}}_{\mathrm{A}}={\mathrm{u}}_{\mathrm{A}}-{\mathrm{u}}_{\mathrm{B}} \\ \Rightarrow {\mathrm{v}}_{\mathrm{B}}={\mathrm{v}}_{\mathrm{A}}+{\mathrm{u}}_{\mathrm{A}}+{\mathrm{u}}_{\mathrm{B}} \end{gathered}$$

$\Rightarrow {\mathrm{v}}_{\mathrm{B}}=4+10-(-20)=34\mathrm{m}/\mathrm{s}$

So the final velocity of B is in the opposite direction of its initial velocity.