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Question

# A man wants to reach point B on the opposite bank of a river flowing at a speed u as shown in figure. what minimum speed relative to water should the man have so that he can reach point B?

A

2u
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B

3u
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C

u3
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D

u2
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Solution

## The correct option is D u√2Let v be the speed of the man in still water. Resultant of v and u should be along AB. Components of →vb (absolute velocity of boatman) along x and y direction are, vx=u−vsinθ and vy=vcosθ Further, tan45∘=vyvx Substituting the values, ⇒1=vcosθu−vsinθ ⇒v=usinθ+cosθ ⇒v=u√2(1√2sinθ+1√2cosθ) ⇒v=u√2(cos45∘sinθ+sin45∘cosθ) ⇒v=u√2sin(θ+45o)...(1) v is minimum at, θ+45o=90o ∴θ=45o So, from equation (1), we get vmin=u√2 Why this question? This question checks the application of motion of 2-D in river-boat problems.

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