Question

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

• A. 2u
• B. u/2
• C.
• D.

Answer 1

The correct option is C

Let v be the speed of boatman in still water.

Resultant of v and u should be along AB. Component of ${\overrightarrow{v}}_b$ (absolute velocity of xboatman) along x and y- direction are,

$v_x=u-vsin\theta and{v}_y=vcos\theta Further,tan{45}^0=\frac{v_y}{v_x}1=\frac{vcos\theta }{u-vsin\theta }\therefore v=\frac{u}{sin\theta +cos\theta }=\frac{u}{\sqrt{2}sin(\theta +{45}^0)}\text{v is minimum at,}\theta +{45}^0={90}^{0}or\theta ={45}^{0}and{v}_{min}=\frac{u}{\sqrt{2}}$