A boat which has a speed of `5 km` per hour in still water crosses a river of width 1 km along the shortest possible path in fifteen minutes. The velocity of the river water in km per hour is :-

Options

A. 1 km/h
B. 3 km/h
C. 4 km/h
D. 5 km/h

Answer

B

Explanation

`u : upsilon_(rg)` (Velocity of river w.r.t. ground)
`upsilon : upsilon_(mr)` (velocity of boat w.r.t. river)

To solve problems, cvovert all velocities with respect to the ground.
`x:(upsilon sin theta-u)t=0 rArr sin theta = (u)/(upsilon)`
`y:d=upsilon cos theta t rArr (d)/(upsilon cos theta)=(d)/(upsilon sqrt(1-sin^(2)theta))`
`=(d)/(upsilon sqrt(1-(u^(2))/(upsilon^(2))))=(d)/(sqrt(upsilon^(2)-u^(2)))`
`t=15 min =1(5)/(60)=(1)/(4)h`
`t=(d)/(sqrt(upsilon^(2)-u^(2))) rArr (1)/(2) = (1)/(sqrt(5^(2)-u^(2)))`
`u=3km//h`