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 then time to cross the river $=\frac{l}{v\cos \theta }$
Drift of boat,
$x=(2v-v\sin \theta )\frac{l}{v\cos \theta }$


For $x$ to be minimum,
$\frac{dx}{d\theta }=0=(2\sec \theta \tan \theta -{\sec }^2\theta )l$
or $\sin \theta =\frac{1}{2}$
or $\theta ={30}^{\circ }$ and $\varphi =90+30={120}^{\circ }$
Hence option (d) is the correct answer.