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 160 square feet is 31,800 pounds when the plane is going 90 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 an airplane wing can be found using the joint variation formula f = k * a * v^2. By solving for the constant k with given values and applying it to the new velocity, we can calculate the new lifting force.

Step-by-step explanation:

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. Using the provided information that a wing with an area of 160 square feet has a lift of 31,800 pounds at a velocity of 90 miles per hour, we can set up an equation to determine the lifting force when the velocity is changed to 230 miles per hour.

First, we express the joint variation as f = k * a * v^2, where k is the variation constant. Given, f = 31,800 pounds, a = 160 square feet, and v = 90 miles per hour, we can solve for k:

k = f / (a * v^2) = 31,800 / (160 * 90^2)

Once we find the value of k, we use it to calculate the new lifting force when the plane's velocity is v = 230 miles per hour. We substitute the values back into the joint variation equation:

f = k * a * v^2f = (31,800 / (160 * 90^2)) * 160 * 230^2

After performing the calculation, we get the new lifting force for the increased velocity.