A boat is sent across a river with a velocity of $8 {kmh}^{-1}$. If the resultant velocity of the boat is $10 {kmh}^{-1}$, the river is flowing with a velocity of

The boat's velocity is the perpendicular component across the river, while the river's velocity is the parallel component, and the resultant velocity is the hypotenuse of this right triangle. Using the Pythagorean theorem, the velocity of the river squared equals the resultant velocity squared minus the boat's velocity squared. Substituting the given values gives 10 squared minus 8 squared, which is 36, and taking the square root gives the river velocity as 6 km/h.

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