A rigid ball of mass $m$ strikes a rigid wall at ${60}^{\circ }$ and gets reflected without loss of speed as shown in the figure. The value of impulse imparted by the wall on the ball will be

 

Given, $p_i=p_f=mV$ Change in momentum of the ball $={\overrightarrow{p}}_f-{\overrightarrow{p}}_i$

$$\begin{gathered} =\left(-p_{fx}\hat{i}-p_{fy}\hat{j}\right)-\left(p_{ix}\hat{i}-p_{iy}\hat{j}\right) \\ =-\hat{i}\left(p_{fx}+p_{ix}\right)-\hat{j}\left(p_{fy}-p_{iy}\right) \\ =-2p_{ix}\hat{i}=-mV\hat{i} \left[p_{fy}-p_{iy}=0\right] \end{gathered}$$  

Here, $p_{ix}=p_{fx}=p_i\cos {60}^{\circ }=\frac{mV}{2}$

 Impulse imparted by the wall $=$ change in the momentum of the ball $=mV$