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Question

# A swimmer wishes to cross a 1km wide river flowing at 5kmhâˆ’1. his speed in still waters is 3kmhâˆ’1. He has to reach directly opposite in minimum possible time. If he does not reach directly opposite by swimming, he has to walk that distance at 5kmhâˆ’1. Find the time taken.

A
0.36hr
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B
0.66hr
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C
1hr
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D
1.36hr
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Solution

## The correct option is D 0.66hr letθbetheanglebetweentherelativeveloctiyofboatandalineperpendiculartotheflow.timetakentocrosstherivert1=13cosθtimetakentowhilewalkingt2=drift5=15(5−3sinθ3cosθ)totaltimet=13cosθ+15(5−3sinθ3cosθ)dtdθ=0⇒sinθ=0.3⇒t=0.66hrs

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