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 76.5 N, Jill pulls with 87.1 N in the northeast direction, and Jane pulls to the southeast with 133 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

Let's caculate the forces aong x-axis

Fx = 76.6 + 87.1cos 45 + 133 cos45 = 232.13 N apprx

Fy = 87.1 sin 45 - 133 sin 45 = 61.589 - 94.045 = -32.456 N apprx

magnitude of the net force = srqroot( {232.13 }^2 + {32.456}^2) = 234.39 N apprx

tan (theta) = 32.456/ 232.13

angle = - 82.042 degree apoprx with respect to east ( lying in south east)

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