Question

a ball of mass 450 g strikes a rigid wall in such a way that it gets deflected by an angle of 60. its speed remains unchanged. The impulse imparted by the wall is 12.4 N. what is the initial a velocity with which the ball strikes the wall

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{initial}\mathrm{velocity}=\mathrm{u} \\ \mathrm{The}\mathrm{initial}\mathrm{momentum}=\mathrm{mu} \\ \mathrm{Momentum}\mathrm{after}\mathrm{striking}\mathrm{the}\mathrm{wall}=\mathrm{mu}\cos (180-60)°=\mathrm{mu}\cos 120°° \\ \mathrm{Impulse}\mathrm{imparted}=\mathrm{change}\mathrm{in}\mathrm{momentum}=\mathrm{mucos}120°-\mathrm{mu}=-\frac{\mathrm{mu}}{2}-\mathrm{mu} \\ \mathrm{But}\mathrm{impulse}=12.4,\mathrm{therefore}, \\ \frac{-3\mathrm{mu}}{2}=12.4 \\ \mathrm{or}\frac{0.45\times 3\mathrm{u}}{2}=12.4 \\ \mathrm{or}\mathrm{u}=\frac{12.4\times 2}{0.45\times 3}=\frac{1240\times 2}{45\times 3}=18.37\mathrm{m}/\mathrm{s} \\ Herenegativesignisomittedbecausetheimpulseisfoundinthedirection \\ ofreflection,sonegativesignisdroppedformagnitudeofvelocity. \end{gathered}$$