Question

A man swims from a point $A$ on one bank of a river of width $100m$. When he swims perpendicular to the water current, he reaches the other bank $50m$ downstream. The angle to the bank at which he should swim, to reach the directly opposite point $B$ on the other bank is

• A. ${10}^{\circ }$ upstream
• B. ${20}^{\circ }$ upstream
• C. ${30}^{\circ }$ upstream
• D. ${60}^{\circ }$ upstream

Answer 1

The correct option is D ${60}^{\circ }$ upstream

$\tan \theta =\frac{v_w}{v_m}=\frac{50}{100}=\frac{1}{2}$ or $v_m=2v_w$
Refer to Fig.
$\sin \alpha =\frac{v_w}{v_m}=\frac{v_m}{2v_w}=\frac{1}{2}$ or $\theta ={30}^{\circ }$
So, it is ${60}^{\circ }$ upstream.