Question

A boat moves relative to water with a speed which is 1/n times the river flow speed.At what angle to the stream direction be boat move to monimize drifting

Answer 1

sin theta =(Vm/Vr)
sin theta = (1/n)
theta = arcsin(1/n)
from steam direction angle will be
90-arcsin(1/n).



thanks for asking.

Answer 2

Answer:

The correct answer is 90° - arcsin(1/n)

Explanation:

Let Vr be the velocity of river.

Let the velocity of boat be Vb = Vr/n

Net drift velocity v = Vr + Vb×cosθ

⇒v= Vr + (Vr/n)×cosθ = Vr×(1+cosθ/n)

Let the velocity along y axis be Vy= Vb×sinθ

w= Vb×sinθ×t

⇒d = Vr×(1+cosθ/n) × w/Vbsinθ

For minimum drift, the first derivative should be equal to zero.

[-n cosecθcotθ - cosec²θ]= 0

Solving the above equation we get the answer as 90° - arcsin(1/n).

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