A boat is sent across a river with a velocity of $8$ km/hr. If the resultant velocity of boat is $10$ km/hr, then velocity of the river is

The boat's sent velocity acts as the perpendicular component across the river, while the river's velocity acts parallel to the banks. Using the Pythagorean theorem for the resultant velocity, the velocity of the river squared equals the resultant velocity squared minus the boat's velocity squared. Substituting the given values gives the river's velocity squared as 10 squared minus 8 squared, which is 36. Taking the square root of 36 gives the river velocity as 6 km/hr.

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