If it takes 1409 foot-pounds of work for a 50 pound force to move an object a distance of 30 feet along a horizontal sidewalk, then at what angle relative to the sidewalk is the force being applied to the object? Round your answer to the nearest degree.

To determine the angle at which the force is applied, we can use the work-energy principle, which states that the work done is equal to the force applied times the distance moved in the direction of the force.

Given:
- Work done (W) = 1409 foot-pounds
- Force (F) = 50 pounds
- Distance (d) = 30 feet

The work done can be expressed as:
\[
W = F \cdot d \cdot \cos(\theta)
\]
where \(\theta\) is the angle between the force and the direction of motion.

We can rearrange the formula to solve for \(\cos(\theta)\):
\[
\cos(\theta) = \frac{W}{F \cdot d}
\]

Now, substituting the values:
\[
\cos(\theta) = \frac{1409}{50 \cdot 30}
\]
\[
\cos(\theta) = \frac{1409}{1500} \approx 0.9393
\]

Next, we find \(\theta\) by taking the arccosine:
\[
\theta = \cos^{-1}(0.9393) \approx 20.9^\circ
\]

Rounding to the nearest degree gives:
\[
\theta \approx 21^\circ
\]

Thus, the angle at which the force is being applied is approximately **21 degrees** relative to the sidewalk.

### Questions for Further Exploration:
1. How does the angle of the applied force affect the efficiency of work done?
2. What would happen if the force was applied vertically instead of at an angle?
3. How would the work change if the distance was increased to 50 feet?
4. What other factors can affect the total work done on the object?
5. How can we calculate the vertical and horizontal components of the force?

### Tip:
To analyze forces at angles, remember to always resolve them into their horizontal and vertical components for clearer calculations.

Explore how to calculate the angle at which a force is applied using the work-energy principle. Given 1409 foot-pounds of work with a 50 pound force over 30 feet, learn to find the angle of application, rounded to the nearest degree.

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