Question

A man can row a boat $4km/hr$ in still water. He is crossing a river where the current is $2km/hr$. If the width of the river is $4km$ , the time taken by him to reach a point directly opposite to him is

• A. $\frac{5\sqrt{7}}{4}hr$
• B. $\frac{4\sqrt{3}}{5}hr$
• C. $\frac{2}{\sqrt{3}}hr$
• D. $\frac{3\sqrt{2}}{4}hr$

Answer 1

The correct option is C $\frac{2}{\sqrt{3}}hr$



From the diagram,
$\sin \theta =\frac{V_r}{V_{br}}=\frac{2}{4}=\frac{1}{2}$
$\Rightarrow \theta ={30}^{\circ }$
Time $t=\frac{\text{Width of river}}{\text{Component of velocity perpendicular to the direction of flow}}$ $\Rightarrow t=\frac{d}{V_b}$
$\Rightarrow t=\frac{d}{4\cos \theta }=\frac{4}{4\cos {30}^{\circ }}=\frac{2}{\sqrt{3}}hr$

Alternate sol:
$t=\frac{AB}{V_{br}}=\frac{BC}{V_r}=\frac{AC}{V_b}$
$\Rightarrow t=\frac{d}{V_b}=\frac{4}{\sqrt{4^2-2^2}}=\frac{2}{\sqrt{3}}hr$