A boat which has a speed of 5 km h - 1 in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water in km h - 1 is

Step-by-step solution

Vertical displacement = 1   km t = 15 60 = 1 4   h ∴       V b cos θ =     1     ( 1 4 ) = 4   km   h − 1 ⇒ cos θ = 4 V b = 4 5 ⇒ sin θ = 3 5 By velocity triangle ABC, sin θ = V r V b ∴       V r V b = 3 5 ⇒ V r 5 = 3 5 ⇒ V r = 3   km   h − 1