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 be swim? [image:3_image107.jpeg]

Question

Dr. Abubacker · Accepted Answer

(b) Let $v$ be the speed of boatman is still water.
[image:3_image198.emf]
Resultant of $v$ and $u$ should be along $AB$. Components of ${\overrightarrow{v}}_{b}$ (absolute velocity of boatman)along $x$ and $y$ direction are,
$v_{x} = u - v\ $sin$	heta$
Further, $	an{45{^\circ}} = \frac{v_{y}}{v_{X}}$
or 1=$\frac{v\ cos	heta}{u - v\ sin	heta}$
$v = \frac{u}{\sin	heta + \cos	heta} = \frac{u}{\sqrt{2}sin(	heta + 45{^\circ})}$
$v$ is minimum at,
$	heta + 45{^\circ} = 90{^\circ}$ or $	heta = 45{^\circ}$
and $v_{\min} = \frac{u}{\sqrt{2}}$

Q. 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 be swim?

Explanation

Reviewed by Dr. Abubacker

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