Question

question 9 of 15, step 1 of 1
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 210 square feet is 17,300 pounds when the plane is going 80 miles per hour. find the lifting force on the wing if the plane speeds up to 170 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.)
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Explanation:

Step1: Write the joint - variation formula

Since \(F\) varies jointly as \(A\) and \(v^{2}\), the formula is \(F = kAv^{2}\), where \(k\) is the variation constant.
We know that \(F = 17300\) pounds, \(A=210\) square feet, and \(v = 80\) miles per hour.
Substitute these values into the formula: \(17300=k\times210\times80^{2}\).

Step2: Solve for \(k\)

First, calculate \(80^{2}=6400\).
The equation becomes \(17300 = k\times210\times6400\).
Then \(k=\frac{17300}{210\times6400}\).
\(k=\frac{17300}{1344000}\approx0.012872\).

Step3: Find \(F\) when \(A = 210\) and \(v = 170\)

Now use the formula \(F=kAv^{2}\) with \(k\approx0.012872\), \(A = 210\), and \(v = 170\).
First, calculate \(v^{2}=170^{2}=28900\).
Then \(F=0.012872\times210\times28900\).
\(F = 0.012872\times6069000\).
\(F\approx78143\)

Answer:

\(78143\)