Question

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

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

Answer 1

Answer: (D)

${120}^{\circ }$

Let boat moves at an angle $\theta$ to the normal as shown in figure, then the time to cross the river $=\frac{l}{v\cos \theta }$
drift $x=(2v-v\sin \theta )\frac{l}{v\cos \theta }$
for $x$ to be minimum $\frac{dx}{d\theta }=0or(2\sec \theta \tan \theta -{\sec }^2\theta )=0$
$or\sin \theta =\frac{1}{2}or\theta ={30}^{o}and\varphi =90+30={120}^o$