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Question

# A river flows 3 km h−1 and a man is capable of swimming 2 km h−1. He wishes to cross it such that displacement parallel to river is minimum. In which direction will he swim?

A
sin1(23)
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B
cos1(23)
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C
tan1(23)
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D
cot1(23)
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Solution

## The correct option is A sin−1(23)Let us assume that he swims at an angle θ with the perpendicular as shown. If river is lm wide time taken to cross it. t=l2cosθ,vx=3−2sinθ horizontal distance covered along x direction during this period. x=vxt=(3−2sinθ)l2cosθ for x to be min dxdθ=0, or l[32secθtanθ−sec2θ]=0 or sinθ=23

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