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 84.3 N, Jill pulls with 77.3 N in the northeast direction, and Jane pulls to the southeast with 137 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

In the north south direction the net force
=77.3 sin 45- 137 sin 45
= - 60*sin 45
= - 42.43 N

In the East direction the net force
= 84.3 + 77.3 cos 45 + 137 cos 45 = 235.83 N

The resultant of these two forces square root of (42.43^2 + 235.83^2)= 239.62 N

The direction is given by 239.62 sin = 235.83
Or 239.62 cos = - 42.43

or tan = - 235.83/ 42.43

=-79.80°.

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