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

Question

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, 1 km h - 1, 3 km h - 1, 4 km h - 1, 41 km h –1

MARKS App · Accepted Answer

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

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