The projectile motion of a particle of mass 5 g is shown in the figure. The initial velocity of the

Question

The projectile motion of a particle of mass 5 g is shown in the figure. The initial velocity of the particle is $5 \sqrt{2} \mathrm{~m}^{-1}$ and the air resistance is assumed to be negligible. The magnitude of the change in momentum between the points $A$ and $B$ is $x 	imes 10^{-2} \mathrm{~kg} \mathrm{~m} \mathrm{~s}^{-1}$. The value of $x$, to the nearest integer, is ___

Professor PC Thomas Classes · Answer

(5) : Change in momentum between the points $A$ and $B$,\ \ $\Delta \vec{p}=\vec{p}_{B}-\vec{p}_{A}$\ Here, $\vec{p}_{A}=m\left(u \cos 45^{\circ} \hat{i}+u \sin 45^{\circ} \hat{j}ight)$\ and $\vec{p}_{B}=m\left(u \cos 45^{\circ} \hat{i}-u \sin 45^{\circ} \hat{j}ight)$\ $	herefore \Delta \vec{p}=-2 m u \sin 45 \hat{j}$\ or $|\Delta \vec{P}|=2 	imes 5 	imes 10^{-3} 	imes 5 \sqrt{2} 	imes \frac{1}{\sqrt{2}}$\ $=5 	imes 10^{-2} \mathrm{~kg} \mathrm{~m} \mathrm{~s}^{-1}$\