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 240 square feet is 39,600 pounds when the plane is traveling at 110 miles per hour.

Find the lifting force if the speed is 230 miles per hour. Round your answer to the nearest integer if necessary.

Option 1: 198,000 pounds
Option 2: 99,000 pounds
Option 3: 396,000 pounds
Option 4: 49,500 pounds

By applying the joint variation formula, we calculate the lifting force when the plane's speed is 230 miles per hour to be approximately 171,972 pounds. This answer does not match any of the provided options, suggesting possible errors in the question.

Explanation:

The problem states that 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. This represents a form of joint variation, which can be represented by the equation f = kav², where k is the constant of variation.

From the given scenario, we know that the lift of a wing with an area of 240 square feet is 39,600 pounds when the plane is going at 110 miles per hour. From this we can find the value of k, which will be the same for other measurements involving the same wing. Using the given lift (f) and velocity (v), we get k = f / (a * v²) = 39,600 / (240 * 110²) ≈ 0.013.

Now we can find the lifting force when the velocity is 230 miles per hour. Substitute a = 240, v = 230, and k ≈ 0.013 into the equation f = kav², we get f = 0.013 * 240 * 230² = 171972, rounded to the nearest integer, we get f ≈ 171,972 pounds. None of the provided options match this answer. Therefore, the problem may contain a mistake or the question may need to be revised.

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