A toy wagon is pulled by exerting a force of 20 pounds on a handle that makes a 30° angle with the horizontal (see figure below). Find the work done in pulling the wagon 20 feet. (Round your answer to one decimal place.)

To calculate the work done, we use the formula for work:

\[
W = F \cdot d \cdot \cos(\theta)
\]

Where:
- \(W\) is the work done,
- \(F\) is the force applied,
- \(d\) is the distance moved,
- \(\theta\) is the angle between the force and the direction of movement, and
- \(\cos(\theta)\) is the cosine of the angle.

In this case:
- \(F = 20\) pounds,
- \(d = 20\) feet,
- \(\theta = 30^\circ\).

First, calculate \(\cos(30^\circ)\):

\[
\cos(30^\circ) = \frac{\sqrt{3}}{2} \approx 0.866
\]

Now, substitute the values into the formula:

\[
W = 20 \cdot 20 \cdot 0.866
\]

Let's calculate this.

\[
W = 20 \cdot 20 \cdot 0.866 = 346.4 \, \text{foot-pounds}
\]

So, the work done in pulling the wagon 20 feet is approximately **346.4 foot-pounds**.

Would you like more details, or do you have any questions?

Here are some related questions:
1. What happens to the work done if the angle is increased to 45°?
2. How would the work change if the force applied was doubled?
3. Can you calculate the work done if the handle made a 0° angle (i.e., pulling horizontally)?
4. What is the effect of increasing the distance to 30 feet on the work done?
5. How would the result differ if the force was measured in Newtons instead of pounds?

**Tip:** When calculating work, the angle used must always be between the direction of the force and the direction of motion.

A toy wagon is pulled by exerting a force of 20 pounds on a handle that makes a 30° angle with the horizontal. Find the work done in pulling the wagon 20 feet. (Round your answer to one decimal place.)

Find the work done in pulling a toy wagon using a force of 20 pounds at a 30° angle over 20 feet. This problem demonstrates the application of work and energy formulas with trigonometric principles, suitable for high school students.

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