If `v=u/2`, in which direction the man should swim so that his drift along the flow is minimum and find value of the minimum drift.

Explanation

`(v_(m//g))_(x)=v sin theta-u =u/2 sin theta-u`
`(v_(m//g))_(y)=v cos theta =u/2 cos theta`

`y:d=u/2 cos theta timplies t=(2d)/(u cos theta)`
`x:x =(u-u/2 sin theta) t=(u-u/2 sin theta)(2d)/(u cos theta)`
`=2d( sec theta-(tan theta)/2)`
For `x` to be minimum
`(dx)/(d theta)=(sec theta tan theta-1/2 sec^(2) theta)=0`
`sec theta= 2 tan theta`
`1/(cos theta)=2 (sin theta)/(cos theta) implies sin theta=1/2 implies theta=30^(@)`
`x_(min)=2d(sec30^(@)-(tan 30^(@))/2)`
`2d(2/(sqrt(3))-1/(2sqrt(3)))=2d((4-1)/(2sqrt(3)))=sqrt(3)d`