Multiple choice

A boat crosses a river with a velocity of 8 km/h. If the resulting velocity of boat is 10 km/h then the velocity of river water is

  1. 4 km/h

  2. 6 km/h

  3. 8 km/h

  4. 10 km/h
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B Correct answer
Explanation

The resulting velocity is the vector sum of the boat velocity and river velocity. Assuming the boat crosses perpendicular to the flow, the resulting velocity squared is (boat velocity)^2 + (river velocity)^2. 10^2 = 8^2 + v_r^2, so 100 = 64 + v_r^2, v_r^2 = 36, v_r = 6 km/h.

AI explanation

The river velocity, boat velocity, and resultant velocity form a right-angled triangle, so by the Pythagorean theorem the river velocity is the square root of the resultant velocity squared minus the boat velocity squared. Substituting the given values gives the square root of 10 squared minus 8 squared, which equals the square root of 36, resulting in 6 km/h.

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