A man is pulling on a rope with a force of 85 N
directed at an angle of 51◦
to the horizontal.
What is the x-component of this force?
Answer in units of N.
005 (part 2 of 2) 10.0 points
What is the y-component of this force?
Answer in units of N

To find the x- and y-components of the force, we’ll use trigonometric functions based on the given angle.

Given:
- Force, \( F = 85 \, \text{N} \)
- Angle to the horizontal, \( \theta = 51^\circ \)

### X-Component of the Force
The x-component (horizontal component) of the force can be found using:
\[
F_x = F \cdot \cos(\theta)
\]
\[
F_x = 85 \cdot \cos(51^\circ)
\]

Calculating this, we get:
\[
F_x \approx 85 \cdot 0.6293 \approx 53.49 \, \text{N}
\]

### Y-Component of the Force
The y-component (vertical component) of the force can be found using:
\[
F_y = F \cdot \sin(\theta)
\]
\[
F_y = 85 \cdot \sin(51^\circ)
\]

Calculating this, we get:
\[
F_y \approx 85 \cdot 0.7771 \approx 66.05 \, \text{N}
\]

### Answers
1. **X-component**: \( F_x \approx 53.49 \, \text{N} \)
2. **Y-component**: \( F_y \approx 66.05 \, \text{N} \)

Would you like a step-by-step breakdown of the calculations?

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#### Related Questions:
1. How does changing the angle affect the x- and y-components?
2. What would the components be if the force was increased to 100 N?
3. How would we find the resultant force if given both components?
4. How do we interpret negative components in this context?
5. What are common applications of breaking down forces into components?

#### Tip:
Always use trigonometric functions based on angle orientation (relative to horizontal or vertical) for accurate component values.

A man is pulling on a rope with a force of 85 N directed at an angle of 51° to the horizontal. What is the x-component of this force? Answer in units of N. What is the y-component of this force? Answer in units of N.

Learn how to find the x and y components of an 85 N force applied at a 51° angle to the horizontal using trigonometric functions. This problem demonstrates vector breakdown with step-by-step solutions, suitable for students in Grades 9-12.

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