Question

the lifting force, f, exerted on an airplane wing varies jointly as the area, a, of the wings surface and the square of the planes velocity, v. the lift of a wing with an area of 170 square feet is 2,300 pounds when the plane is going at 130 miles per hour. find the lifting force if the speed is 220 miles per hour. round your answer to the nearest integer if necessary.

Explanation:

Step1: Write the joint - variation formula

The joint - variation formula is $F = kAv^{2}$, where $F$ is the lifting force, $A$ is the area of the wing's surface, $v$ is the velocity of the plane, and $k$ is the constant of variation.
We know that $F = 2300$ pounds, $A = 170$ square feet, and $v = 130$ miles per hour. Substitute these values into the formula:
$2300=k\times170\times130^{2}$

Step2: Solve for the constant of variation $k$

First, calculate $130^{2}=16900$. Then the equation becomes $2300 = k\times170\times16900$.
$2300=k\times2873000$.
$k=\frac{2300}{2873000}=\frac{23}{28730}$

Step3: Find the lifting force when $v = 220$ miles per hour

Now, we want to find $F$ when $A = 170$ square feet and $v = 220$ miles per hour.
Substitute $k=\frac{23}{28730}$, $A = 170$, and $v = 220$ into the formula $F = kAv^{2}$.
First, calculate $v^{2}=220^{2}=48400$.
$F=\frac{23}{28730}\times170\times48400$
$F=\frac{23\times170\times48400}{28730}$
$F=\frac{23\times170\times4840}{2873}$
$F=\frac{23\times822800}{2873}$
$F=\frac{18924400}{2873}$
$F\approx6607$

Answer:

$6607$