A rigid ball of mass $m$ strikes a rigid wall at $60^{\circ}$ and gets reflected without loss of spe

Question

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\

Professor PC Thomas Classes · Answer

(a) : Given, $p_{i}=p_{f}=m V$ Change in momentum of the ball $=\vec{p}_{f}-\vec{p}_{i}$\ $=-\left(p_{f x} \hat{i}-p_{f y} \hat{j}ight)-\left(p_{i x} \hat{i}-p_{i y} \hat{j}ight)$\ $=-\hat{i}\left(p_{f x}+p_{i x}ight)-\hat{j}\left(p_{f y}-p_{i y}ight)$\ $=-2 p_{i x} \hat{i}-0 \hat{j}=-m V \hat{i}$\ Here, $p_{i x}=p_{f x}=p_{i} \cos 60^{\circ}=\frac{m V}{2}$\ $\because \quad$ Impulse imparted by the wall $=$ change in the momentum of the ball $=m V$.\