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 290 square feet is 3000 pounds when the plane is going 250 miles per hour. Find the lifting force on the wing if the plane slows down to 210 miles per hour. (Leave the variation constant in fraction form or round to at least 5 decimal places. Round off your final answer to the nearest pound.)

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 290 square feet is 3000 pounds when the plane is going 250 miles per hour. Find the lifting force on the wing if the plane slows down to 210 miles per hour. (Leave the variation constant in fraction form or round to at least 5 decimal places. Round off your final answer to the nearest pound.)

Answer 1

We are given that the lifting force, F, varies jointly with the area, A, and the square of the velocity, v. This can be represented as an equation:

F = k * A * v^2,

where k is the variation constant.

To find the value of k, we can use the given information when the lift is 3000 pounds and the area is 290 square feet with a velocity of 250 miles per hour. Plugging in these values into the equation, we get:

3000 = k * 290 * (250^2).

Simplifying this equation, we find:

k = 3000 / (290 * 250^2).

Now, we can use this value of k in the equation to find the new lifting force when the velocity is 210 miles per hour. Plugging in the values of A = 290, v = 210, and the value of k we just found, we get:

F = (3000 / (290 * 250^2)) * 290 * (210^2).

After simplifying this equation, the lifting force is approximately 1710 pounds. Rounding this off to the nearest pound, the lifting force on the wing when the plane slows down to 210 miles per hour is 1710 pounds.