A man can swim at a speed of `3 km h^-1` in still water. He wants to cross a `500-m` wide river flowing at `2 km h^-1`. He keeps himself always at an angle to `120^@` with the river flow while swimming.
The time taken to cross the river is.

Options

A. `(3)/(2) h`
B. `(1)/(6) h`
C. `(1)/(3 sqrt(3)) h`
D. none

Answer

C

Explanation

( c) `t = (d)/( v sin theta) =(0.5 km)/(3 sin 120^@ km h^-1)=(1)/(3 sqrt(3)) h`
`x = (u + v cos theta) t = (2 + 3 cos 120^@)(1)/(3 sqrt(3)) = (1)/(6 sqrt(3))`.