A boat which has a speed of `5 km// hr ` in steel water crosses a river of width ` 1 km` along the shortest possible path in `15 minutes`. The velocity of the river water in ` km// hr` is

Options

A. 3 km/hr
B. 4 km/hr
C. 5 km/hr
D. 2 km/hr

Answer

A

Explanation

`V_(mr)=5km//hr`
t=15 min
`t=d/sqrt(V_(mr)^(2)-V_(r)^(2)) implies 15/60= 1/sqrt(25-V_(r)^(2))`
`implies 4 = sqrt(25-V_(r)^(2)) implies V_(r)^(2) = 25-16 implies V_(r)^(2) = 9`
`implies V_(r) = 3 km//hr`