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The problem from the image describes a scenario involving forces at an angle. Michelle is swinging on a tire tied to a tree branch, with Elwin pulling her back. The problem asks to find the tension in the rope, given that the force pulling Michelle and the tire is 825 N, and the rope makes an angle of 30.0 degrees with the vertical.

### To solve this:
We can break the tension \( T \) in the rope into two components:
1. Vertical component: \( T_y = T \cdot \cos(\theta) \), which balances the weight of Michelle and the tire (since gravity pulls her down).
2. Horizontal component: \( T_x = T \cdot \sin(\theta) \), which balances the pulling force (825 N) applied by Elwin.

Since Elwin's pulling force equals the horizontal component of the tension:
\[
T_x = 825 \, \text{N} = T \cdot \sin(30^\circ)
\]
Thus:
\[
825 = T \cdot 0.5
\]
\[
T = \frac{825}{0.5} = 1650 \, \text{N}
\]

The tension in the rope is **1650 N**.

Would you like more details on the solution or any clarifications? Here are 5 additional questions you could explore:

1. How would the tension change if the angle increased or decreased?
2. What if the pulling force was greater than 825 N?
3. How would the problem change if the rope were at a different angle, like 45 degrees?
4. What forces are acting on Michelle and the tire besides the tension in the rope?
5. How does the angle of the rope affect the vertical and horizontal components of the tension?

**Tip:** When dealing with forces at an angle, always break the forces into vertical and horizontal components to analyze the system effectively.

If gravity pulls on Michelle and the tire with a force of 825 N, and Elwin pulls Michelle back far enough for the rope to make an angle of 30.0 degrees with the vertical, what is the tension in the rope supporting Michelle and the tire?

Learn how to calculate the tension in a rope when forces are applied at an angle. In this example, Michelle is being pulled with a force of 825 N, and the rope forms a 30-degree angle with the vertical. Find out the tension using trigonometric formulas and force balance equations. Suitable for high school students in Grades 10-12.

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