A boat moves relative to water with a velocity which is n=2.0 times less than the river flow velocity. At what angle to the stream direction must the boat move to minimize drifting?
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a
300
b
600
c
900
d
1200
answer is D.
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Detailed Solution
When the velocity of river is greater than the velocity of boot or swimmer, then the motion of boat or swimmer without drifting is not possible νr→ velocity of the river flow ; OA=ℓ width of the riverν→ velocity of the boat w.r.t still water and νr=nνθ→ angle made by the boat with the river flow.Fromm figureDrift (x) =(νcosθ+νr)t→(1)OA=ℓ=νsinθt→(2)From (1) & (2) we get, x=(cotθ+νrνsecθ)ℓ for x to be minimumwith θdxdθ=0⇒cosθ=−1n=−12⇒θ=1200