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 $8km$, the time taken by him to cross with zero drift is

• A. $\frac{8}{\sqrt{3}}hr$
• B. $\frac{2\sqrt{3}}{3}hr$
• C. $\frac{4}{\sqrt{3}}hr$
• D. $\frac{3\sqrt{2}}{8}hr$

Answer 1

The correct option is C $\frac{4}{\sqrt{3}}hr$


From the diagram,
$\sin \theta =\frac{V_r}{V_{br}}=\frac{2}{4}=\frac{1}{2}$
⇒$\theta ={30}^{\circ }$

$\text{Time (t)}=\frac{\text{Width of river}}{\text{Component of velocity perpendicular to the direction of flow}}$
$t=\frac{d}{V_b}=\frac{w}{4\cos \theta }=\frac{8}{4\cos {30}^{\circ }}=\frac{8}{2\sqrt{3}}hr$