Question

A river is flowing from W to E with a speed of $5\text{m/min}$. A man can swim in still water with a velocity $10\text{m/min}$. In which direction should the man swim so as to take the shortest possible path to go to the south.

• A. ${30}^{\circ }$ with downstream
• B. ${60}^{\circ }$ with downstream
• C. ${120}^{\circ }$ with downstream
• D. South

Answer 1

The correct option is C ${120}^{\circ }$ with downstream


For shortest possible path man should swim with an angle $(90+\theta )$ with downstream.
From the fig.
$\sin \theta =\frac{v_r}{v_m}=\frac{5}{10}=\frac{1}{2}$
$\Rightarrow \therefore \theta ={30}^{\circ }$
So angle with downstream
${90}^{\circ }+{30}^{\circ }={120}^{\circ }$