Ball A is about to hit a wall at an angle of  incidence of $\mathrm{\theta }={30}^{\circ }$. But before hitting the wall  it made a head on collision with another identical 
ball B. The ball B then collides with the wall. The  coefficient of restitution for collision between two balls is ${\mathrm{e}}_1=0.8$ and that between a ball and  
the wall ${\mathrm{e}}_1=0.6$ Find the final velocity of ball  B. Initial velocity of A was $\mathrm{u}=5{\mathrm{ms}}^{-1}$Neglect  friction $\left[{\tan }^{-1}\left(\frac{2.25}{2.34}\right)={44}^{\circ }\right]$
 

or collision of A and B
$$\begin{gathered} {\mathrm{V}}_{\mathrm{B}}-{\mathrm{V}}_{\mathrm{A}}={\mathrm{e}}_1\left({\mathrm{u}}_{\mathrm{A}}-{\mathrm{u}}_{\mathrm{B}}\right) \\ {\mathrm{V}}_{\mathrm{B}}-{\mathrm{V}}_{\mathrm{A}}=0.8\times 5=4 ..............\left(1\right) \\ \text{ and }{\mathrm{mV}}_{\mathrm{B}}+{\mathrm{mV}}_{\mathrm{A}}=\mathrm{mu} \\ {\mathrm{V}}_{\mathrm{B}}+{\mathrm{V}}_{\mathrm{A}}=5 ........... \left(2\right) \end{gathered}$$

Solving (1) and (2) we get 
      ${\mathrm{V}}_{\mathrm{B}}=4.5{\mathrm{ms}}^{-1};{\mathrm{V}}_{\mathrm{A}}=0.5{\mathrm{ms}}^{-1}$
Now B collides with the wall.

Velocity component parallel to the wall remains unchanged.

${\mathrm{V}}_{11}={\mathrm{V}}_{\mathrm{B}}\sin {30}^{\circ }=2.25\mathrm{m}/\mathrm{s}$
Velocity component perpendicular to the wall becomes 
${\mathrm{V}}_{\perp }={\mathrm{e}}_2{\mathrm{V}}_{\mathrm{B}}\cos {30}^{\circ }=0.6\times 4.5\times \frac{\sqrt{3}}{2}=2.34\mathrm{m}/\mathrm{s}$
If final velocity makes an angle with normal to the wall
$\tan \mathrm{\alpha }=\frac{2.25}{2.34}\Rightarrow \mathrm{\alpha }\simeq {44}^{\circ }\text{ and }\mathrm{V}=\sqrt{2{.25}^2+2{.34}^2}=3.24\mathrm{m}/\mathrm{s}$