Question

A motorboat travelling at $10m/s$ due North, encounters a current travelling at $5m/s$ due East. Find the magnitude of relative velocity of boat with respect to the current.

• A. $10\sqrt{2}\text{m/s}$
• B. $5\sqrt{5}\text{m/s}$
• C. $10\sqrt{5}\text{m/s}$
• D. $5\sqrt{10}\text{m/s}$

Answer 1

The correct option is B $5\sqrt{5}\text{m/s}$


Let ${\overrightarrow{V}}_b=10\hat{j}$ and ${\overrightarrow{V}}_c=5\hat{i}$ be the velocities of boat and current respectively.

By definition,
${\overrightarrow{V}}_{bc}={\overrightarrow{V}}_b-{\overrightarrow{V}}_c=10\hat{j}-5\hat{i}=-5\hat{i}+10\hat{j}$
$|{\overrightarrow{V}}_{bc}|=\sqrt{{10}^2+5^2}=5\sqrt{5}\text{m/s}$