Question

A boat is moving with a velocity of $3\hat{i}+4\hat{j}$ with respect to the ground. The water in the river is moving with a velocity of $-3\hat{i}-4\hat{j}$ with respect to the 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. $5\sqrt{2}$

Answer 1

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

Given velocity of boat wrt ground ${\overrightarrow{v}}_{\text{bg}}=3\hat{i}+4\hat{j}$
velocity of water wrt ground
${\overrightarrow{v}}_{\text{wg}}=-3i-4j$
Now velocity of boat wrt water ${\overrightarrow{v}}_{\text{bw}}={\overrightarrow{v}}_b-{\overrightarrow{v}}_w$
$v_{\text{bw}}=3\hat{i}+4\hat{j}-(-3\hat{i}-4\hat{j})$
$v_{\text{bw}}=6\hat{i}+8\hat{j}$