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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 sin1(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=32sinθ
horizontal distance covered along x direction during this period x=vx×t.
x=(32sinθ)l2cosθ
for x to be minimum dxdθ=0, or
l[32secθtanθsec2θ]=0 or
sinθ=23
129853_134039_ans_b3236ffdc5e7415cae31f4b0dc753ac2.png

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