# The projectile motion of a particle of mass

Question:

The projectile motion of a particle of mass $5 \mathrm{~g}$ is shown in the figure.

The initial velocity of the particle is

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

Solution:

(5)

$|\overrightarrow{\mathrm{u}}|=|\overrightarrow{\mathrm{v}}| \ldots(1)$

$\overrightarrow{\mathrm{u}}=\mathrm{u} \cos 45 \hat{\mathrm{i}}+\mathrm{u} \sin 45 \hat{\mathrm{j}} \cdots(2)$

$\overrightarrow{\mathrm{v}}=v \cos 45 \hat{\mathrm{i}}-\mathrm{v} \sin 45 \hat{\mathrm{j}} \cdots(3)$

$|\overrightarrow{\Delta \mathrm{P}}|=|\mathrm{m}(\overrightarrow{\mathrm{v}}-\overrightarrow{\mathrm{u}})| \ldots(4)$

$\Delta \mathrm{P}=2 \mathrm{mu} \sin 45^{\circ}$

$=2 \times 5 \times 10^{-3} \times 5 \sqrt{2} \times \frac{1}{\sqrt{2}}$

$=50 \times 10^{-3}$

$=5 \times 10^{-2}$