Question

A ball of mass $m$ travelling with velocity $(3\hat{i}+4\hat{j})\text{m/s}$ receives an impulse $J=-(2m\widehat{)}i\text{N-s}$. The magnitude of velocity of the ball immediately after receiving impulse is

• A. $\sqrt{17}m/s$
• B. $\sqrt{41}m/s$
• C. $4m/s$
• D. $5m/s$

Answer 1

The correct option is A $\sqrt{17}m/s$

Given:
mass of ball; $m$
Initial velocity; $v_i=(3\hat{i}+4\hat{j})\text{m/s}$
Impulse, $J=-\left(2m\right)\hat{i}\text{N-s}$

Impulse, $\left(J\right)=\Delta P=m\left(v_f\right)-m\left(v_i\right)=m(v_f-v_i)$
$-2m\hat{i}=m(v_f-(3\hat{i}+4\hat{j}\left)\right)$
$v_f=\hat{i}+4\hat{j}\text{m/s}$
$\left|v_f\right|=\sqrt{1^2+4^2}=\sqrt{17}\text{m/s}$