Three people pull simultaneously on a stubborn donkey. Jack pulls directly ahead

Question

Three people pull simultaneously on a stubborn donkey. Jack pulls directly ahead of the donkey with a force of 70.9 N, Jill pulls with 67.5 N in a direction 45° to the left, and Jane pulls in a direction 45° to the right with 173 N. (Since the donkey is involved with such uncoordinated people, who can blame it for being stubborn?) Find the magnitude of the net force the people exert on the donkey.What is the direction of the net force? Express this as the angle from straight ahead between 0° and 90°, with a positive sign for angles to the left and a negative sign for angles to the right.

Explanation / Answer

Let's call "directly ahead" the x-axis.

Fx = 70.9N + 67.5N*cos45 + 173N*cos-45 =240.9 N

Fy = 0 + 67.5N*sin45º + 173N*sin-45º = -74.59N

|F| = (Fx² + Fy²) = 252.15 N magnitude

= arctan(Fy/Fx) = arctan(-74.59/240.9) = -17.0º direction

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