Calculating Net Force on a Stubborn Donkey

When three people pull simultaneously on a stubborn donkey, the net force they exert must be calculated to determine the overall effect on the donkey. In this scenario, Jack pulls directly ahead of the donkey with a force of 63.1 N, Jill pulls with 64.5 N in a direction 45° to the left, and Jane pulls in a direction 45° to the right with 167 N.

To find the magnitude of the net force, we need to calculate the components of each force in the x and y directions. The x-component is the force multiplied by the cosine of the angle, and the y-component is the force multiplied by the sine of the angle. Adding up the x-components and y-components separately, we can then use the Pythagorean theorem to find the magnitude of the net force.

The x-components are: 63.1 N * cos(0) + 64.5 N * cos(45°) + 167 N * cos(-45°) = 63.1 N + 45.54 N + 117.98 N = 226.62 N.

The y-components are: 0 + 64.5 N * sin(45°) - 167 N * sin(-45°) = 45.54 N - 117.98 N = -72.44 N.

Using the Pythagorean theorem, the magnitude of the net force is √(226.62 N^2 + (-72.44 N)^2) = √(61315.32 N^2) ≈ 247.60 N.

To find the angle of the net force, we can use the inverse tangent function: θ = tan^(-1)(-72.44 N / 226.62 N) ≈ -18.56°.

Therefore, the magnitude of the net force exerted on the stubborn donkey by Jack, Jill, and Jane is approximately 247.60 N, and the direction of the net force is approximately -18.56° to the right. Despite the uncoordinated efforts of the people involved, the donkey is subjected to a significant net force in a specific direction.