Question

A boat moves relative to water with a velocity $v$ and river is flowing with $2v$. At what angle will the boat move with the stream to have minimum drift ?

• A. ${30}^{\circ }$
• B. ${60}^{\circ }$
• C. ${90}^{\circ }$
• D. ${120}^{\circ }$

Answer 1

The correct option is D ${120}^{\circ }$


Let the boat move at angle $\theta$ to the normal as shown in the figure.

Time to cross the river $=\frac{l}{v\cos \theta }$

Drift of boat will be,

$x=(2v-v\sin \theta )\frac{l}{v\cos \theta }$

For $x$ to be minimum,

$\frac{dx}{d\theta }=0=(2\sec \theta \tan \theta -{\sec }^2\theta )l$

$\Rightarrow \sin \theta =\frac{1}{2}$

$\therefore \theta ={30}^{\circ }$

So, $\varphi =90+30={120}^{\circ }$

Hence, option $\left(\text{D}\right)$ is the correct answer.