Question

A boat is moving with a velocity $3\hat{i}+4\hat{j}$ with respect to ground. The water in the river is moving with a velocity $-3\hat{i}-4\hat{j}$ with respect to ground. The relative velocity of the boat with respect to water is

• A. $8\hat{j}$
• B. $-6\hat{i}-8\hat{j}$
• C. $6\hat{i}+8\hat{j}$
• D. $6\hat{i}-8\hat{j}$

Answer 1

The correct option is C $6\hat{i}+8\hat{j}$

The relative velocity of boat w.r.t to water is given as
$\overrightarrow{V_{bw}}=\overrightarrow{V_b}-\overrightarrow{V_w}$
Given, $\overrightarrow{V_b}=3\hat{i}+4\hat{j}$, $\overrightarrow{V_w}=-3\hat{i}-4\hat{j}$
Thus, we have
$\overrightarrow{V_{bw}}=(3\hat{i}+4\hat{j})-(-3\hat{i}-4\hat{j})=6\hat{i}+8\hat{j}$