Question

A ball is moving with an initial velocity $30\hat{i}\text{m/s}$ towards a wall oriented at an angle such that the velocity of the ball after collision with the wall becomes $-30\hat{j}\text{m/s}$. If mass of the ball is $0.5\text{kg}$, then the magnitude of the impulse imparted by the wall is

• A. $0\text{N.s}$
• B. $30\text{N.s}$
• C. $15\text{N.s}$
• D. $15\sqrt{2}\text{N.s}$

Answer 1

The correct option is D $15\sqrt{2}\text{N.s}$

From impulse momentum theorem on the ball,
$\text{Impulse}=\text{change in momentum}$
$\overrightarrow{J}=m\overrightarrow{v_f}-m\overrightarrow{v_i}$


$\overrightarrow{J}=m(-30\hat{j})-m\left(30\hat{i}\right)$
$\overrightarrow{J}=-15\hat{j}-15\hat{i}$
($\because m=0.5\text{kg}$)
Hence, magnitude of impulse imparted by wall is,
$|\overrightarrow{J}|=\sqrt{(-15{)}^2+(-15{)}^2}$
$\therefore |\overrightarrow{J}|=15\sqrt{2}\text{N.s}$