A boat moves relative to water with a velocity which is `n=2.0` times less than the river flow velocity. At what angle to the stream direction must the boat move to minimize drifting?

Answer

`theta=arcsin(1//eta)+pi//2=120^@`

Explanation

Let `v_0` be the stream velocity and `v^'` the velocity of boat with respect to water. A `(v_0)/(v^')=eta=2gt0`, some drifting of boat is inevitable.
Let `vecv` make an angle `theta` with flow direction. (Figure), then the time taken to cross the rive
`t=(d)/(v^'sin theta)` (where d is the width of the river)
In this time interval, the drifting of the boat
`x=(v^'cos theta+v_0)t`
`=(v^'costheta+v_0)(d)/(v^'sin theta)=(cot theta+eta cosec theta)d`
For `x_(min)` (minimum drifting)
`(d)/(dtheta)(cot theta+eta cosec theta)=0`, which yields
`cos theta=-1/eta=-1/2`
Hence, `theta=120^@`