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

4

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3

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1

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\sqrt{4}

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Solution

The correct option is B $3$
According to data,
Boat speed $= 5 k m / h r$
Shortest distance covered $= 1 k m$
Time Taken $= 15 m i n = 0.25 h r$

The given figure represents the Triangle Vector Diagram.
Speed of the boat in moving water $= \frac{d i s t a n c e}{t i m e} = \frac{1}{0.25} = 4 k m / h r$
In vector right angled triangle ABC:
$\to A B^{2} + \to B C^{2} = \to A C^{2}$
$\Rightarrow∣ \to A B^{2} ∣= 25 - 16 = 9 k m / h r$
$\Rightarrow∣ \to A B^{2} ∣= 3 k m / h r$
Velocity of river $= 3 k m / h r$

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

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