Question

A man wants to reach a point B on the opposite bank of the river flowing at speed u. What minimum speed relative water should the man have so that he can reach point B. In which direction should he swim?

Answer 1

The resultant u ad v should be along the line AB.

                             V = velocity of Man

                             $V_x=u-Vsin\theta\\ V_y=Vcos\theta\\ tan (45deg) = V_y /V_x\\1=Vcos\theta/u-Vsin\theta$

Hence,                  $V=u/sin\theta+cos\theta=u/\sqrt{2}sin(\theta+45)$

Since V is minimum at, θ + 45° = 90°

Therefore,            $V_{min} =u /\sqrt2$