A boat moves relative to water with a velocity half of the river flow velocity if the angle from the direction of flow with which boat must move relative to stream directly to minimize drift is $\frac{2 \times π}{n}$ , then n is:

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Solution

The correct option is B 3
Velocity of Boat $\Rightarrow v_{x} = 2 v - v sin (θ) v_{y} = v cos (θ)$
Time required to cross the river $t = \frac{d}{r cos (θ)}$
Since $v_{x} > 0$ So drift can't be $0$
Drift $= v_{x} \times t = (2 v - v sin (θ)) \times \frac{d}{v cos (θ)}$
$\frac{d x}{d θ} = 0$
$\Rightarrow \frac{d}{v} (2 v sec (θ) tan (θ)) - v s e c^{2} (θ) = 0 \Rightarrow 2 v sin (θ) = v \Rightarrow θ = 30 °$
$∴$ Vertical angle $= 30 °$
Now, $120 = \frac{2 π}{3} r a d i a n$
Hence $x = 3$

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A boat moves relative to water with a velocity half of the river flow velocity if the angle from the direction of flow with which boat must move relative to stream directly to minimize drift is 2×πn, then n is:

A boat moves relative to water with a velocity half of the river flow velocity if the angle from the direction of flow with which boat must move relative to stream directly to minimize drift is $\frac{2 \times π}{n}$ , then n is: