Question

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 280 square feet is 16,400 pounds when the plane is going 110 miles per hour. find the lifting force on the wing if the plane speeds up to 230 miles per hour. (leave the variation constant in fraction form or round to at least 5 decimal places

Answer 1

The lifting force on the wing when the plane speeds up to 230 miles per hour is approximately 71,699.17 pounds.

We can express the relationship between the lifting force, area, and velocity using the following equation:

F = k × A × V²

where:

F is the lifting force (pounds)

A is the area of the wing's surface (square feet)

V is the plane's velocity (miles per hour)

k is a constant of proportionality

We are given that the lifting force of a wing with an area of 280 square feet is 16,400 pounds when the plane is going 110 miles per hour. We can use this information to solve for the constant of proportionality k. Plugging in the given values, we get:

16400 = k × 280 × 110²

Solving for k, we get:

k ≈ 0.0454

Now, we can use this value of k to calculate the lifting force on the wing when the plane speeds up to 230 miles per hour. Plugging in the new velocity, we get:

F = 0.0454 × 280 × 230² ≈ 71,699.17 pounds