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This problem describes a situation where wind resistance \( r \) varies jointly as surface area \( a \) and velocity \( v \). Mathematically, this means:

\[
r = k \cdot a \cdot v
\]

where \( k \) is the constant of proportionality.

### Step 1: Find the constant \( k \)

We are given that for an object traveling at 22 mph with a surface area of 15 square feet, the wind resistance is 220 Newtons. Using the formula, we can plug these values in to find \( k \):

\[
220 = k \cdot 15 \cdot 22
\]

Now, solve for \( k \):

\[
k = \frac{220}{15 \cdot 22}
\]

### Step 2: Solve for the unknown velocity \( v \)

Once we find \( k \), we use it to find the velocity \( v \) for the second scenario, where the wind resistance is 275 Newtons, the surface area is 20 square feet, and we need to find the velocity:

\[
275 = k \cdot 20 \cdot v
\]

Now, let's calculate these values. I'll compute \( k \) and then use it to find \( v \).The constant of proportionality \( k \) is approximately \( 0.667 \). Using this value, the velocity \( v \) for the car with a surface area of 20 square feet to experience a wind resistance of 275 Newtons is approximately \( 20.63 \) mph.

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. How does increasing surface area affect wind resistance?
2. What happens to wind resistance if velocity doubles?
3. Can we use this equation for other fluid resistances, such as in water?
4. How would the wind resistance change if the car's velocity were halved?
5. How is this concept applied in vehicle aerodynamics design?

**Tip:** In joint variation problems, always identify all variables involved and establish the relationship before solving.

Wind resistance r varies jointly as an object's surface area a and its velocity v. If an object traveling at 22 miles per hour with a surface area of 15 square feet experiences a wind resistance of 220 Newtons, how fast must a car with 20 square feet of surface area travel in order to experience a wind resistance of 275 Newtons?

Learn how to solve a joint variation problem involving wind resistance, surface area, and velocity. Given wind resistance at specific conditions, calculate the velocity required for a different surface area to experience a different wind resistance. Suitable for high school students.

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