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The problem asks to find the speed of the wind \( r \) in miles per hour when the windmill is producing 500 watts of power, using the given formula:

\[
r = \sqrt[3]{\frac{P}{0.02}}
\]

Where:
- \( P \) is the power in watts (given as 500 watts),
- \( r \) is the speed of the wind in miles per hour.

We need to substitute \( P = 500 \) into the equation and solve for \( r \).

Let me calculate that for you.The speed of the wind \( r \), when the windmill is producing 500 watts of power, is approximately 29.24 miles per hour.

Would you like more details or have any further questions?

Here are 5 related questions:
1. How does the speed of the wind affect the power output of a windmill?
2. What happens to the windmill's power if the wind speed doubles?
3. Can you derive a formula for the power \( P \) in terms of the wind speed \( r \)?
4. What would the wind speed be if the power produced was 1,000 watts?
5. How does the constant 0.02 in the formula relate to the windmill's efficiency?

**Tip:** Cubic root functions appear in many physics applications where one variable grows or shrinks in proportion to the cube of another, such as in energy or volume relationships.

The power generated by a windmill is related to the speed of the wind by the formula, where r is the speed of the wind in miles per hour and P is the power (in watts). Find the speed (r) when the windmill is producing 500 watts of power.

Solve the windmill power generation problem using the formula r = (P / 0.02)^(1/3). Learn how to find the wind speed in miles per hour when the power output is 500 watts. Suitable for high school students, Grades 9-12.

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