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A boat moves relative to water with a ve...

A boat moves relative to water with a velocity which is `n=2.0` times less than the river flow velocity. At what angle to the stream direction must the boat move to minimize drifting?

A

`pi // 2`

B

`sin^(-1)(1//n)`

C

`(pi)/(2)+ sin^(-1)(1//n)`

D

`(pi)/(2)-sin^(-1)(1//n)`

Text Solution

Verified by Experts

The correct Answer is:
C
Let width of the river be d speed of strcam be v and
the speed of the boat reltive to water be u and the
angle with the verticle at which the boat must move for
minimum drifting is `theta` .
Time taken to cross the river = `(d)/(u cos theta)`
Drift of the boat is (v-usin `theta`) `(d// u cos theta)`
Differentiating this w.r.t. time and equating to zero we
get the angle `theta` for minimum drifting as `sin^(-1)(u/v)`
Angle with the direction of the stream is
`90^(@)+sin ^(-1)(u/v)`
Here u = `v/n`
`:. "Angle"=(pi)/(2)+ sin^(-1)(1/(n))`
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