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. $5\sqrt{2}\hat{j}$

Answer 1

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

Given, velocity of boat w.r.t. ground $V_{bg}=3\hat{i}+4\hat{j}$
and, velocity of river water $V_{wg}=-3\hat{i}-4\hat{j}$
$\therefore$ Relative velocity of boat with respect to river water is given by
$V_{bw}=V_{bg}-V_{wg}=(3\hat{i}+4\hat{j})-(-3\hat{i}-4\hat{j})$
$=6\hat{i}+8\hat{j}$