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A boat is sent across a river with a velocity of 8 km h⁻¹. If the resultant velocity of boat is 10 km h⁻¹, then the velocity of the river is

1. 12.8 km h⁻¹
2. 6 km h⁻¹
3. 8 km h⁻¹
4. 10 km h⁻¹

Correct answer: 6 km h⁻¹

Solution

The resultant velocity of the boat and river forms the hypotenuse of a right triangle, with the boat's velocity and river's velocity as the perpendicular sides. Using the Pythagoras theorem: (resultant velocity)² = (boat's velocity)² + (river's velocity)². Substituting values: 10² = 8² + (river's velocity)², solving gives river's velocity = 6 km/h.

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