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3. The wind exerts a force of 452 N north on a sailboat, while the water

exerts a force of 325 N west on the sailboat. Find the magnitude and
direction of the net force on the sailboat.​

User Aneroid
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1 Answer

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Step-by-step explanation:

The two forces form a right triangle.

The magnitude is found with Pythagorean theorem.

F² = Fx² + Fy²

F² = (-325 N)² + (452 N)²

F = 557 N

The direction is found with trigonometry:

θ = atan(Fy / Fx)

θ = atan(452 N / -325 N)

θ = -54.3° or 125.7°

θ is 125.7° from the +x axis (east). That corresponds to a direction of 35.7° west of north, or 54.3° north of west.

The net force has a magnitude of 557 N and a direction of 35.7° west of north.

User Xplora
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