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Given |Vbr| = 4 m//s = magnitude of velo...

Given `|V_br| = 4 m//s =` magnitude of velocity of boatman with respect to river, `v_r= 2 m//s` in the directior shown. Boatman wants to reach from point A to point B. At what angle `theta` should he row his boat ?

A

`u, 45^(@)` North-West

B

`u, 45^(@)` North-East

C

`(u)/(sqrt(2)), 45^(@)` North-West

D

`(u)/(sqrt(2)), 45^(@)` North-East

Text Solution

Verified by Experts

The correct Answer is:
C
Let `upsilon` be the speed boatman in still water. Resultant of `upsilon` and u should be along AB. Components of `v_(b)` (absolute velocity of boatman) along x and y directions are,

`upsilon_(x)=u-upsilon sin theta` and `upsilon_(y)=upsilon cos theta`
Further, `tan 45^(@)=(upsilon_(y))/(upsilon_(x))` or `1=(upsilon cos theta)/(u-upsilon sin theta)`
`therefore upsilon=(u)/(sin theta+cos heta)=(u)/(sqrt(2)sin(theta+45^(@)))`
`upsilon` is minimum at,
`theta+45^(@)=90^(@)` or `theta = 45^(@)` and `upsilon_(min)=(u)/(sqrt(2))`
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