Question

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

• A. $6\hat{i}+8\hat{j}$
• B. $0$
• C. $6\hat{i}-8\hat{j}$
• D. $-6\hat{i}+8\hat{j}$

Answer 1

Answer: (A)

$6\hat{i}+8\hat{j}$

$\overrightarrow{v}=$ Velocity of boat wrt ground $=3\hat{i}+4\hat{j}$
$\overrightarrow{u}=$ Velocity of water wrt ground $=-3\hat{i}-4\hat{j}$
${\overrightarrow{V}}_{BW}=$ Relative velocity of boat w.r.t. water.
${\overrightarrow{V}}_{BW}=\overrightarrow{v}-\overrightarrow{u}$
So, ${\overrightarrow{V}}_{BW}=(3\hat{i}+4\hat{j})-(-3\hat{i}-4\hat{j})=6\hat{i}+8\hat{j}$