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Question

# A river flows 3 km/h and a man is capable of swimming at the rate of 2 km/h. He wishes to cross it such that the displacement parallel to river is minimum. In which direction should 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 he swims at an angle θ with the perpendicular as shown in figure.If the river is lm wide, time taken to cross it,t=l2cosθ,vx=3−2sinθhorizontal distance covered along x direction during this period x=vx×t.x=(3−2sinθ)l2cosθfor x to be minimum dxdθ=0, orl[32secθtanθ−sec2θ]=0 orsinθ=23

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