Q. A boat having a speed of 5 km/h in still water,crosses a river of width 1 km along the shortest possible path in 15 minutes. The speed of the river in km/h is: A) 1 B) 3 C) 4 D√41
The speed of the boat in still water is 5 km/h. The boat crosses the river that has a width of 1 km along the shortest path possible in 15 minutes. The length of the shortest path in this case is 1 km.
Let the speed of the river be S. And the boat moves at 5 km/h at an angle `theta` to the line perpendicular to the direction of flow of water. As the boat takes 15 minutes to cross the river, its speed across the river is 4 km/h. The velocity of the boat can be divided into two components, one against the direction of flow of water and the other perpendicular to the direction in which the water flows. The former is `5*sin theta` and the latter is `5*cos theta` .
`5*cos theta = 4`
=> `theta = cos^-1(4/5)`
The speed of the river is `5*sin theta` = `5*sin(cos^-1(4/5))` = 3 km/h
The speed of the river is 3 km/h.