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A person is rowing across the river with a velocity of 4. 5 km/hr northward. The river is flowing eastward at 3. 5 km/hr. What is the magnitude of her velocity (v) with respect to the shore?

User Jill
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1 Answer

19 votes
19 votes

The velocity of the rower relative to the shore is the sum of her velocity relative to the water and the velocity of the water relative to the shore:


\vec v_(R/S) = \vec v_(R/W) + \vec v_(W/S)

Then


\vec v_(R/S) = \left(4.5(\rm km)/(\rm h),0\right) + \left(0,3.5(\rm km)/(\rm h)\right) = (4.5,3.5)(\rm km)/(\rm h)

The magnitude of this velocity is

√(4.5² + 3.5²) m/s ≈ 5.7 m/s

User Statler
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