Question

In the previous problem, the man wants to cross the river in the minimum time. In which directions, he should move? Find the minimum time to cross the river and his displacement (drift) along the flow.

Answer 1

`y: d=v cos theta t`
`t=d/(v cos theta)`
`t` will be minimum if `cos theta` is maximum.
`(cos theta)_(max)=1`
`t` will be minimum if ` cos theta` is maximum.
`(cos theta)_(max)=1`
`implies theta=0^(@)`
To cross the river in the minimum time, the man should swim perpendicular to the river flow.

`(v/(m//g))_(x)=u, (v_(m//g))_(y)=v`
`y:d=vt implies t=t_(min)=d/v`
`x:x=ut=(ud)/v`
`x`: drift along the flow