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`
B. `3`
C. 4
D. `sqrt(41)`

Answer

B

Explanation

Shortest route corresponds to`vec(v)_(b)` perpendicular to river flow
`:. t = (d)/(v_(b)) = (d)/(sqrt(v_(br)^(2) - v_(r)^(2))) `
or `1/4 = (d)/(sqrt(25-v_(r)^(2)))`
rArr `v_(r) = 3 km//h`