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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
$\frac{{mv}}{2}$
$\;\frac{{mv}}{3}$
$mv$
$2mv$
Solution
$\begin{array}{l}
\,\,\,\,\,\,\,\,Given,\,{P_i} = {P_f} = mV\\
chenge\,in\,momentum\,of\,the\,ball\\
= \,{{\bar P}_f} – {{\bar P}_i}\\
= \left( { – {P_{fx}}\hat i – {P_{fy}}\hat j} \right) – \left( {{P_{ix}}\hat i – {P_{iy}}\hat j} \right)\\
= – \hat i\left( {{P_{fx}} + {p_{ix}}} \right) – \hat j\left( {{p_{fy}} – {p_{iy}}} \right)\\
= – 2{P_{ix}}\hat i = – mV\hat i\,\,\,\left[ {{P_{fy}} – {P_{iy}} = 0} \right]
\end{array}$
$\begin{array}{l}
Here,\,{P_{ix}} = {P_{fx}} = {P_i}\cos {60^ \circ } = \frac{{mV}}{2}\\
{\rm{Impulse}}\,{\rm{imparted}}\,{\rm{by}}\,{\rm{the}}\,{\rm{wall}}\,\\
= change\,in\,the\,momentum\,of\\
the\,ball\, = \,mV.
\end{array}$
