Question

A small sphere of mass m = 2kg moving with a velocity $\overline{u}=\widehat{4i}-7\hat{j}m/s$ collides with a smooth wall and returns with a velocity $\overline{v}=\hat{i}-3\hat{j}m/s$. The magnitude of the impulse received by the ball is

• A. $5kgm{s}^{-1}$
• B. $10kgm{s}^{-1}$
• C. $20kgm{s}^{-1}$
• D. $15kgm{s}^{-1}$

Answer 1

The correct option is B $10kgm{s}^{-1}$

Impulse is equal to the change in momentum.

$J=m\Delta v$

$\Delta v=\overrightarrow{v}-\overrightarrow{u}=(\hat{i}-3\hat{j})-(4\hat{i}-7\hat{j})=-3\hat{i}+4\hat{j}$

$J=2(-3\hat{i}+4\hat{j})$

Magnitude of J$=2\sqrt{(-3{)}^2+4^2}=2\times 5=10kgm{s}^{-1}$.