A heavy sheet of wood and a light ball is moving towards each other as shown in the figure. What will be the speed of the ball after collision?

$\overline{V_2}=\left(\frac{(1+e)m_1}{m_1+m_2}\right)\overline{u_1}+\left(\frac{m_2-e{m}_1}{m_1+m_2}\right)\overline{u_2}$

Given,

$\begin{array}{l}{m}_1=M\\ m_2=m\end{array}$ & M >>m

$\Rightarrow m<<M \frac{m}{M} \left(or\right) \frac{m_2}{m_1} \approx 0$

$\therefore \overline{V_2}=\frac{(1+e)}{1+\frac{m_2}{m_1}}\overline{u_1}+\left(\frac{\frac{m_2}{m_1}-e}{1+\frac{m_2}{m_1}}\right)\overline{u_2}$

$\overline{V_2}=(1+e)\overline{u_1}+e\overline{u_2}$

$=(1+\frac{1}{3})\left(2V\right)-\frac{1}{3}(-V)=\frac{8V+V}{3}=3V$