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Question

# A boat moves relative to water with a velocity half of the river flow velocity if the angle from the direction of flow with which boat must move relative to stream directly to minimize drift is 2×πn, then n is:

A
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B
0
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C
4
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D
3
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Solution

## The correct option is B 3Velocity of Boat ⇒vx=2v−vsin(θ)vy=vcos(θ)Time required to cross the river t=drcos(θ)Since vx>0 So drift can't be 0Drift =vx×t=(2v−vsin(θ))×dvcos(θ)dxdθ=0⇒dv(2vsec(θ)tan(θ))−vsec2(θ)=0⇒2vsin(θ)=v⇒θ=30°∴ Vertical angle =30°Now, 120=2π3radianHence x=3

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