A river is flowing from west to east direction with speed of 9 . If a boat capable of moving at a maximum speed of 27 in still water, crosses the river in half a minute, while moving with maximum speed at an angle of 150° to direction of river flow, then

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Solution

Q.
A river is flowing from west to east direction with speed of 9 ${kmh}^{- 1}$ . If a boat capable of moving at a maximum speed of 27 ${kmh}^{- 1}$ in still water, crosses the river in half a minute, while moving with maximum speed at an angle of 150° to direction of river flow, then the width of the river is : [2025]

1 300 m

2 112.5 m

3 75 m

4 $112.5 \times \sqrt{3} m$

Ans.
(2)

Velocity of boat normal to river flow,

$v_{⊥} = 27 \times \cos 60 ° = \frac{27}{2} km / hr$

The width of the river,

$W = v_{⊥} t = \frac{27}{2} \times \frac{5}{18} \times 30 m = 112.5 m$

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