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A ball of mass $m$ moving with velocity $v_0$ collides a wall as shown in figure. After impact it rebounds with a velocity $\frac {3}{4}v_0$. The impulse acting on ball during impact is
$ - \frac{m}{2}\,\,{v_0}\hat j$
$ - \frac{3}{4}\,\,m{v_0}\hat i$
$ - \frac{5}{4}\,\,m{v_0}\hat i$
None of these
Solution
$\overrightarrow{\mathrm{v}}_{\mathrm{i}}=\mathrm{v}_{0} \cos 37^{\circ} \hat{\mathrm{i}}+\mathrm{v}_{0} \sin 37^{\circ} \hat{\mathrm{j}}=\frac{4}{5} \mathrm{v}_{0} \hat{\mathrm{i}}+\frac{3}{5} \mathrm{v}_{0} \hat{\mathrm{j}}$
$\overrightarrow{\mathrm{v}}_{\mathrm{f}}=-\frac{3}{4} \mathrm{v}_{0} \cos 53^{\circ} \hat{\mathrm{i}}+\frac{3}{4} \mathrm{v}_{0} \sin 53^{\circ} \hat{\mathrm{j}}$
$=-\frac{9}{20} \mathrm{v}_{0} \hat{\mathrm{i}}+\frac{3}{5} \mathrm{v}_{0} \hat{\mathrm{j}}$
$\overrightarrow{\mathrm{J}}=\mathrm{m}\left(\overrightarrow{\mathrm{v}}_{\mathrm{f}}-\overrightarrow{\mathrm{v}}_{\mathrm{i}}\right)=-\frac{5}{4} \mathrm{mv}_{0} \hat{\mathrm{i}}$
