Question

A ball moving with speed $v$ in $x$ direction changes its direction and speed. Its speed reduces to $\frac{v}{2}$ in $y-$ direction. Find out the magnitude of the impulse on the ball while the ball changes its direction. [Given mass of the ball is $m$]

• A. $2\sqrt{5}mv$
• B. $\sqrt{5}mv$
• C. $\frac{\sqrt{5}}{2}mv$
• D. $\frac{\sqrt{5}}{4}mv$

Answer 1

The correct option is C $\frac{\sqrt{5}}{2}mv$

Let initial velocity of the ball $=v\hat{i}$
Then, final velocity $=\frac{v}{2}\hat{j}$


Impulse = change in momentum
= final momentum - initial momentum
$=m\frac{v}{2}\hat{j}-mv\hat{i}$
Therefore, $\left|\text{Impulse}\right|=\sqrt{{\left(\frac{mv}{2}\right)}^2+(mv{)}^2}=\sqrt{\frac{5}{4}}mv$
or $\left|J\right|=\frac{\sqrt{5}}{2}mv$