A boat moves relative to water with a velocity which is 1 / n times the river flow velocity. At what angle to the stream direction must the boat move to minimize drifting?

Question

A boat moves relative to water with a velocity which is 1 / n times the river flow velocity. At what angle to the stream direction must the boat move to minimize drifting? (A) π / 2 (B)  sin -1(1 / n ) (C) (π/2)+ sin -1(1 / n ) (D) (π/2)- sin -1(1 / n )

Tardigrade Admin · Accepted Answer

Let width of the river be d speed of stream be

v

and the speed of the boat relative to water be

u

and the angle with the verticle at which the boat must move for minimum drifting is

θ

.
Time taken to cross the river

= \frac{d}{u c o s θ}

Drift of the boat is

(v - u s in θ) (d / u cos θ)

Differentiating this w.r.t time and equating to zero we get the angle

θ

for minimum drifting as

sin^{- 1} (\frac{u}{v})

Angle with the direction of the stream is

9 0^{\circ} + sin^{- 1} (\frac{u}{v})

Here

u = \frac{v}{n}

∴

Angle

= \frac{π}{2} + sin^{- 1} (\frac{1}{n})

Q. A boat moves relative to water with a velocity which is $1/ n$ times the river flow velocity. At what angle to the stream direction must the boat move to minimize drifting?

$π /2$

$sin^{- 1} (1/ n)$

$\frac{π}{2} + sin^{- 1} (1/ n)$

$\frac{π}{2} - sin^{- 1} (1/ n)$

Q. A boat moves relative to water with a velocity which is 1/n times the river flow velocity. At what angle to the stream direction must the boat move to minimize drifting?

π/2

sin−1(1/n)

2π​+sin−1(1/n)

2π​−sin−1(1/n)

Q. A boat moves relative to water with a velocity which is $1/ n$ times the river flow velocity. At what angle to the stream direction must the boat move to minimize drifting?

$π /2$

$sin^{- 1} (1/ n)$

$\frac{π}{2} + sin^{- 1} (1/ n)$

$\frac{π}{2} - sin^{- 1} (1/ n)$