A boat crossing a river moves with a velocity $\to v$ relative to still water. The river is flowing with a velocity $\to v / 2$ 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:

30^{\circ}

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45^{\circ}

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15^{\circ}

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90^{\circ}

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Solution

The correct option is A $30^{\circ}$
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 $v_{o} = \frac{v}{2}$ .

Velocity of boat along the direction of velocity of river will be $v c o s θ + \frac{v}{2}$ .To satisfy the above given condition , component of boat’s velocity along the river’s velocity should be zero.

Therefore, $v c o s θ + \frac{v}{2} = 0$

$c o s θ = \frac{- 1}{2}$

So, the required angle $θ$ is 120 degree. w.r.t. horizontal or 30 degrees w .r. t vertical

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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 boat crossing a river moves with a velocity $\to v$ relative to still water. The river is flowing with a velocity $\to v / 2$ 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: