A rigid ball of mass \(m\) strikes a rigid wall at \(60^o \) 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

\(\begin{array}{l}
\,\,\,\,\,\,\,\,Given,\,{P_i} = {P_f} = mV\\
chenge\,in\,momentum\,of\,the\,ball\\
 = \,{{\bar P}_f} - {{\bar P}_i}\\
 = \left( { - {P_{fx}}\hat i - {P_{fy}}\hat j} \right) - \left( {{P_{ix}}\hat i - {P_{iy}}\hat j} \right)\\
 =  - \hat i\left( {{P_{fx}} + {p_{ix}}} \right) - \hat j\left( {{p_{fy}} - {p_{iy}}} \right)\\
 =  - 2{P_{ix}}\hat i =  - mV\hat i\,\,\,\left[ {{P_{fy}} - {P_{iy}} = 0} \right]
\end{array}\) \(\begin{array}{l}
Here,\,{P_{ix}} = {P_{fx}} = {P_i}\cos {60^ \circ } = \frac{{mV}}{2}\\
{\rm{Impulse}}\,{\rm{imparted}}\,{\rm{by}}\,{\rm{the}}\,{\rm{wall}}\,\\
 = change\,in\,the\,momentum\,of\\
the\,ball\, = \,mV.
\end{array}\)