A man can swim in still water with speed `v`. He wants to cross a river of width `d` that flows with speed `u` and reaches the point directely opposite to his starting point. (a) In which direction should he try to swim (i.e., find the angle the makes with the river flow)? (b) much time will he take to cross the river ?

Explanation

`O`: straight point
`A`: Destination point
To reach to point `A`, the man should swim at an angle `theta` with `OA` as shown.

`(v_(m//g))_(x)=v sin theta-u`
`(v_(m//g))_(y)=v cos theta`
`x`: (uniform motion),displacement `=0`
`x=(v sin theta-u)t=0`
`implies v sin theta=u`
`sin theta=u/vimplies theta=sin^(-1)(u/v)`
`y`: (uniform motion), displacement `=d`
`t=d/(v cos theta)=d/(vsqrt(1-sin^(2) theta))=d/(vsqrt(1-(u^(2))/(v^(2))))=d/(sqrt(v^(2)-u^(2)))`