Question

A boat is moving with a velocity $3\hat{i}-5\hat{j}$ with respect to ground. The water in the river is moving with a velocity $-\hat{i}+2\hat{j}$ with respect to ground. The relative velocity of the boat with respect to water is

• A. $4\hat{i}-7\hat{j}$
• B. $4\hat{i}+5\hat{j}$
• C. $-3\hat{i}-7\hat{j}$
• D. $-2\hat{i}+7\hat{j}$

Answer 1

The correct option is A $4\hat{i}-7\hat{j}$

The relative velocity of boat w.r.t to water is given as
$\overrightarrow{V_{bw}}=\overrightarrow{V_b}-\overrightarrow{V_w}$
Given, $\overrightarrow{V_b}=3\hat{i}-5\hat{j}$, $\overrightarrow{V_w}=-\hat{i}+2\hat{j}$
Thus, we have
$\overrightarrow{V_{bw}}=(3\hat{i}-5\hat{j})-(-\hat{i}+2\hat{j})=4\hat{i}-7\hat{j}$