Three people pull simultaneously on a stubborn donkey. Jack pulls eastward with

Question

Three people pull simultaneously on a stubborn donkey. Jack pulls eastward with a force of 85.7 N, Jill pulls with 62.9 N in the northeast direction, and Jane pulls to the southeast with 187 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 the east direction between 0° and 90°, with a positive sign for north of east and a negative sign for south of east.

Explanation / Answer

From the given data:
Force by Jack, F1 = 85.7 i
Force by Jill, F2 = 62.9/2 i + 62.9/2 j
Force by Jane = 187/2 i - 187/2 j
Net force, F
= F1 + F2 + F3
= 95.7 i + (62.9/2 i + 62.9/2 j) + (187/2 i - 187/2 j)
= 272.4 i - 87.72 j
=> magnitude of net force
= [(272.4)^2 + (87.72)^2]
= 286 N

b)
angle from east to south
angle = arc tan (87.72/272.4)
= - 17.85°.

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