A construction worker attempts to pull a stake out of the ground by pulling on a rope that is attached to the stake and makes an angle of 60.0 degrees with the horizontal. Then worker exerts a force of 125 newtons on the rope. What is the magnitude of the upward component of the force acting on the stake?

The vertical component of the force is Fsin(θ) where F is the force on the rope, and θ is the angle with the horizontal.

To find the magnitude of the upward component of the force acting on the stake, we need to determine the vertical component of the force exerted on the rope.

The vertical component can be found by using trigonometry, specifically the sine function. The equation for the vertical component of a force (F_y) is:

F_y = F * sin(θ)

Where:
F is the magnitude of the force exerted on the rope (125 newtons)
θ is the angle between the force and the horizontal (60.0 degrees)

Substituting the given values into the formula:

F_y = 125 N * sin(60.0 degrees)

To find the sine of 60.0 degrees, we can use a scientific calculator or refer to a trigonometric table. The sine of 60.0 degrees is √3/2 or approximately 0.866.

F_y ≈ 125 N * 0.866
F_y ≈ 108.25 N

Therefore, the magnitude of the upward component of the force acting on the stake is approximately 108.25 newtons.