Question 256 of 308

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

The initial velocity of the particle is $5\sqrt{2}{ms}^{-1}$ and the air resistance is assumed to be negligible. The magnitude of the change in momentum between the points $A$ and $B$ is $x\times {10}^{-2}{kgms}^{-1}$. The value of $x$, to the nearest integer, is ___ .

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Answer: 5

$|\vec{u}|=|\vec{v}|$
$\vec{u}=u\cos 45\hat{i}+u\sin 45\hat{j}$
$\vec{v}=v\cos 45\hat{i}-vsin45\hat{j}$
$|\vec{\Delta P}|=\left|m\left(\vec{v}-\vec{u}\right)\right|$
$\Delta P=2mu\sin 45^{\circ}$$=2\times 5\times {10}^{-3}\times 5\sqrt{2}\times \dfrac{1}{\sqrt{2}}$
$\Delta P=50\times {10}^{-3}$$=5\times {10}^{-2}$.