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Beth, a construction worker, attempts to pull a stake out of the ground by pulling on a rope that is attached to the stake. The rope makes an angle of 69.1 ◦ with the horizontal. If Beth exerts a force of 147.3 N on the rope, what is the magnitude of the upward component of the force acting on the stake?

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Answer:

[tex]F_y=137.61N[/tex]

Explanation:

The force exerted by Beth, has components on the two axes of the xy plane, [tex]Fcos\theta[/tex] on the x axis and [tex]Fsin\theta[/tex] on the y axis, where [tex]\theta[/tex] is the angle formed by the rope with the horizontal and [tex]F[/tex] is the magnitude of the force. So, the magnitude of the upward component of the force acting on the stake, is the force component in the y axis:

[tex]F_y=(147.3N)sin(69.1^\circ)\\F_y=137.61N[/tex]

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