Question

A man can row a boat with a speed of $4\frac{km}{hr}$ in still water. If he is crossing a river where the current is $2\frac{km}{hr},$ and the width of the river is 12 km, 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. $\frac{6}{\sqrt{3}}hr$
• D. $\frac{3\sqrt{2}}{8}hr$

Answer 1

The correct option is C $\frac{6}{\sqrt{3}}hr$


From the diagram, $sin\theta =\frac{V_r}{V_{br}}=\frac{2}{4}=\frac{1}{2}\Rightarrow \theta ={30}^{\circ }$
$Time\left(t\right)=\frac{\text{Width of river}}{\text{component of velocity perpendicular to the direction of flow}}$
$=\frac{d}{V_{br}cos\theta }$
$\Rightarrow t=\frac{w}{4cos\theta }=\frac{12}{4cos{30}^{\circ }}=\frac{12}{2\sqrt{3}}hr.$