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The speed of a boat is 5 km / hr in still water. It crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of river water is :

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$3 km h^{- 1}$

$2 km h^{- 1}$

$5 km h^{- 1}$

$4 km h^{- 1}$

answer is A.

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Detailed Solution

$V_{m} = 5 km {hr}^{- 1}$

$d = 1 km$

$t = 15 \min = \frac{1}{4} hrs$

time in shortest path

$t = \frac{d}{\sqrt{V_{m}^{2} - V_{R}^{2}}} \frac{1}{4} = \frac{1}{\sqrt{5^{2} - V_{R}^{2}}} 5^{2} - V_{R}^{2} = 16 V_{R}^{2} = 9 V_{R}^{} = 3$

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