A Boat Which Has Speed Of 5Km/Hr in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. What is the velocity of the river water in km/h?
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Explanation:
Answer:
velocity of river=3km/hr
time of crossing =width of river/((velocity of boat)^2-(velocity of river)^2)^1/2
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- Speed of the boat in still water = 5 km/hr
- Width of the river (AB) = 1 km
- Time taken by the boat to cross the river = 15 minutes = 1/4 hr
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Let the velocity of the river be x km/hr.
Distance covered by the boat in 15 minutes = 1.25 km
‡ Because of the flow of the river, the boat will move in the direction of AC, which is the shortest possible path for the boat
AC = 1.25 km
AB = 1 km
‡ BC is the other bank of the river so the width AB of the river will be perpendicular to BC.⠀⠀
∠B = 90°
⠀⠀⠀Apply Pythagoras theorem in ΔABC
⠀⠀⠀⠀⠀⠀(AB)² + (BC)² = (AC)²
⠀⠀BC = 0.75 km⠀
✨ So, the distance covered by the river water in 15 minutes is 0.75 km.
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✨Velocity of the river = 3km/hr
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