A boat moves relative to water with a velocity which is $n = 2.0$ times less than the river flow velocity. The angle (in degrees) to the stream direction must the boat move to minimize drifting is (120+x) . The value of x is :

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Solution

Let $v_{0}$ be the stream velocity and $v^{'}$ the velocity of boat with respect to water. At
$\frac{v_{0}}{v^{'}} = η = 2 > 0$ , some drifting of boat is inevitable.
Let ${\to v}^{'}$ make an angle $θ$ with flow direction (shown in figure below), then the time taken to cross the river
$t = \frac{d}{v^{'} sin θ}$ (where $d$ is the width of the river)
In this time interval, the drifting of the boat
$x = (v^{'} cos θ + v_{0}) t$
$= (v^{'} cos θ + v_{0}) \frac{d}{v^{'} sin θ} = (cot θ + η csc θ) d$
For $x_{m i n}$ (minimum drifting)
$\frac{d}{d θ} (cot θ + η csc θ) = 0$ , which yields
$cos θ = - \frac{1}{η} = - \frac{1}{2}$
Hence, $θ = 120^{\circ}$

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A boat moves relative to water with a velocity which is n=2.0 times less than the river flow velocity. The angle (in degrees) to the stream direction must the boat move to minimize drifting is (120+x) . The value of x is :

A boat moves relative to water with a velocity which is $n = 2.0$ times less than the river flow velocity. The angle (in degrees) to the stream direction must the boat move to minimize drifting is (120+x) . The value of x is :