Question

A man can swim at a speed of $3km{h}^{-1}$ in still water, he wants to cross a $500m$ wide river flowing at $2km{h}^{-1}$. He keeps himself always at an angle of ${120}^o$ with the river flow while swimming
Choose the correct options

• A. The time taken to cross the river is $\frac{1}{3\sqrt{3}}h$
• B. The time taken to cross the river is $\frac{1}{2\sqrt{3}}h$
• C. The drift of the man along the direction of flow, when he arrives at the opposite bank is $\frac{1}{6\sqrt{3}}km$
• D. The drift of the man along the direction of flow, when he arrives at the opposite bank is $\frac{1}{3\sqrt{3}}km$

Answer 1

Answer: (A), (C)

The correct options are
A The time taken to cross the river is $\frac{1}{3\sqrt{3}}h$
C The drift of the man along the direction of flow, when he arrives at the opposite bank is $\frac{1}{6\sqrt{3}}km$

We know $v=\frac{d}{t}$

$t=\frac{d}{v}=\frac{\frac{1}{2}}{v\cos {30}^o}=\frac{\frac{1}{2}}{3\frac{\sqrt{1}}{2}}=\frac{1}{3\sqrt{3}}hrs$

as you know indirection the are two velocities one is given & another is velocities components

So $V_{mean}=V_{given}=V_{\sin {30}^{\circ }}$

$=2-3\sin {30}^{\circ }$

$=2-\frac{3}{2}=\frac{1}{2}$

drift $=vt=\frac{1}{2}\times \frac{1}{3\sqrt{3}}=\frac{1}{3\sqrt{3}}km$