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 60.0 degrees with the horizontal. Beth exerts a force of 125 N on the rope. What is the magnitude of the upward component of the force acting on the stake?

108.25N

Well, let me grab my construction hat and bring some laughter to this question.

If Beth is trying to pull out a stake from the ground, she's going to need some "stake"-ing good effort.

Now, let's get serious for a moment. To find the magnitude of the upward component of the force, we need to use trigonometry.

Since the rope makes an angle of 60.0 degrees with the horizontal, we're looking for the vertical component of the force. This component can be calculated using the formula:

Upward Force = Applied Force * sin(angle)

In this case, the applied force is 125 N and the angle is 60.0 degrees. Plugging these values into the formula, we get:

Upward Force = 125 N * sin(60.0 degrees)

Now, let's grab our calculators (or clown noses, for some added fun) and solve this equation!

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 by Beth on the rope.

The upward component of the force acting on the stake can be calculated using trigonometry. We can use the sine function to relate the angle and the vertical component of the force.

The equation is given by:

Upward force = Force on rope * sin(angle)

Given:
Force on rope = 125 N
Angle = 60.0 degrees

Substituting the values into the equation, we have:

Upward force = 125 N * sin(60.0 degrees)

Calculating this using a calculator, we get:

Upward force ≈ 108.25 N

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

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 by Beth.

We can use trigonometry to find this component. The vertical component can be found using the formula:

Vertical Component = Force x sin(θ)

Where:
- Force is the magnitude of the force exerted on the rope (125 N)
- θ is the angle the rope makes with the horizontal (60.0 degrees)

Let's substitute the values into the formula:

Vertical Component = 125 N x sin(60.0)

Using a scientific calculator, we can find that sin(60.0) is approximately 0.86603.

Vertical Component = 125 N x 0.86603

Vertical Component ≈ 108.25375 N

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