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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. What minimum velocity relative to water should the man have so that he can reach directly to point B?

A
u2, in the upstream at an angle 45 with the vertical
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B
2u, in the upstream at an angle 45 with the vertical
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C
u2, in the downstream at an angle 45 with the vertical
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D
2u, in the downstream at an angle 45 with the vertical
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Solution

## The correct option is A u√2, in the upstream at an angle 45∘ with the verticalLet v be the velocity of man w.r.t flow in a direction at an angle θ with the direction perpendicular to flow. For the man to go along AB, Along y-axis, vsin(θ+45∘)=usin45∘ for him to go along AB, then v=usin45∘sin(θ+45∘) For v to be minimum, sin(θ+45∘) should be maximum ⇒θ+45∘=90∘ ⇒θ=45∘ ⇒Vmin=u√2, in the upstream at an angle 45∘ to the vertical.

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