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 71.3 N, Jill pulls with 86.1 N in a direction 45° to the left, and Jane pulls in a direction 45° to the right with 127 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

assuming forward as x - direction

and right as y - direction

Net force = 71.3 i + 86.1 *(cos(45) i + j * sin(45)) + 127 (cos(45) i - j * sin(45))

net force = 222 i - 29 j N

magnitude of force = sqrt(222^2 + 29^2)

magnitude of force = 223.9 N

the magnitude of the net force the people exert on the donkey is 223.9 N

direction = arctan(-29/222)

direction = -7.44 degree

the direction of the net force is 7.44 degree to the left

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