Two ropes are tied to a 50 kg boat. One pulls with a force of 120 N due West and the other rope pulls with a force of 140 N due South. Find the net force of the boat (magnitude and direction) and the acceleration.

The net force on the boat is the vector

F = (-120 N) i + (-140 N) j

where we take West and South to be the negative directions going left-and-right and up-and-down, respectively.

The magnitude of the net force is

F = √((-120 N)² + (-140 N)²) = 20 √(85) N ≈ 180 N

and its direction is

tan(θ) = (-140 N) / (-120 N)   →   θ ≈ -130°

relative to due East, or approximately 50° South of West.

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