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Question

# A boat crossing a river moves with a velocity →v relative to still water. The river is flowing with a velocity →v/2 with respect to the bank. The angle at which the boat should start from the bank with respect to the river, to minimize the drift is:

A
30
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B
45
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C
15
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D
90
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Solution

## The correct option is A 30∘In order to minimise the drift ,the net velocity of the boat should be perpendicular to the velocity of the river.Let the boat moves with velocity u=v in still water and makes an angle Q with velocity of river i.e vo=v2.Velocity of boat along the direction of velocity of river will be vcosθ+v2.To satisfy the above given condition , component of boat’s velocity along the river’s velocity should be zero.Therefore, vcosθ+v2=0cosθ=−12So, the required angle θ is 120 degree. w.r.t. horizontal or 30 degrees w .r. t vertical

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