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Q.

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
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