https://file.aiquickdraw.com/mathbot/file/1728865808978amsukf4r.jpg

The problem involves a relationship where the lifting force \( F \) on an airplane wing varies jointly as the area \( A \) of the wing and the square of the plane's velocity \( v^2 \). We can represent this as a joint variation equation:

\[
F = k \cdot A \cdot v^2
\]

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

### Step 1: Solve for the constant \( k \)
We are given the following information:
- The area of the wing \( A = 250 \) square feet,
- The velocity \( v = 150 \) miles per hour,
- The lifting force \( F = 9,900 \) pounds.

Substitute these values into the variation equation to find \( k \):

\[
9,900 = k \cdot 250 \cdot 150^2
\]

\[
9,900 = k \cdot 250 \cdot 22,500
\]

\[
9,900 = k \cdot 5,625,000
\]

Now, solve for \( k \):

\[
k = \frac{9,900}{5,625,000} \approx 0.00176
\]

### Step 2: Use the constant \( k \) to find the lifting force when the speed is 220 mph
Now, we need to find the lifting force when the speed is \( v = 220 \) mph, using the same wing area \( A = 250 \) square feet.

Substitute \( A = 250 \), \( v = 220 \), and \( k = 0.00176 \) into the equation:

\[
F = 0.00176 \cdot 250 \cdot 220^2
\]

\[
F = 0.00176 \cdot 250 \cdot 48,400
\]

\[
F = 0.00176 \cdot 12,100,000
\]

\[
F = 21,296
\]

### Final Answer:
The lifting force is approximately **21,296 pounds**.

Let me know if you would like further details or explanations!

Here are 5 related questions you can explore:
1. How does the lifting force change if the velocity is doubled?
2. What is the effect of increasing the wing area on the lifting force?
3. How would the lifting force change if the velocity were decreased to 100 mph?
4. What happens to the lifting force if both the area and velocity are doubled?
5. How can this relationship be applied to different types of aircraft with varying wing shapes?

**Tip:** When dealing with joint variation, always isolate the constant first, then substitute the new conditions into the equation to solve for the unknown.

The lifting force, F, exerted on an airplane wing varies jointly as the area, A, of the wing's surface and the square of the plane's velocity, v. The lift of a wing with an area of 250 square feet is 9,900 pounds when the plane is going at 150 miles per hour. Find the lifting force if the speed is 220 miles per hour. Round your answer to the nearest integer if necessary.

Solve a joint variation problem to calculate the lifting force on an airplane wing. The lift of a 250 square foot wing is 9,900 pounds at 150 mph. Learn how to find the lift at 220 mph using algebra and joint variation. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation