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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

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B

u/2

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C

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D

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Solution

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 vb (absolute velocity of xboatman) along x and y- direction are,

vx=uvsin θ and vy=v cos θFurther, tan450=vyvx1=v cos θuv sin θ v=usin θ+cos θ=u2sin(θ+450)v is minimum at,θ+450=900 or θ=450and vmin=u2


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