College Algebra, Chapter 2, 2.5, Section 2.5, Problem 38

According to the aerodynamics principle, the lift $L$ on an airplane wing at take off varies jointly as the squares of the speed $s$ of the plane and the area $A$ of its wings. A plane with a wing area of $500\text{ft}^2$ travelling at $\displaystyle 50 \frac{\text{mi}}{\text{h}}$ experiences a lift of 1700 lb. How much lift would a plane with a wing area of $600\text{ft}^2$ travelling at $\displaystyle 40 \frac{\text{mi}}{\text{h}}$ experience?


$
\begin{equation}
\begin{aligned}
L &= k s^2 A^2\\
\\
1700 \text{lb} &= k \left( 50 \frac{\text{mi}}{\text{h}} \right)^2 \left( 500 \text{ft}^2 \right)^2 && \text{Substitute the given}\\
\\
k &= \frac{1700 \text{lb}}{\left( 50^2 \frac{\text{mi}^2}{\text{h}^2} \right) \left( 500^2 \text{ft}^4 \right)}
\end{aligned}
\end{equation}
$


Then, if $A = 600 \text{ft}^2$ and $\displaystyle s = 40 \frac{\text{mi}}{\text{h}}$

$
\begin{equation}
\begin{aligned}
L &= k s^2 A^2\\
\\
L &= \frac{1700 \text{lb}}{\left( 50^2 \frac{\text{mi}^2}{\text{h}^2} \right) \left( 500 \text{ft}^4 \right)} \left( 40 \frac{\text{mi}}{\text{h}} \right)^2 \left( 600 \text{ft}^2 \right)^2 && \text{Solve for } L \text{, cancel out like terms}\\
\\
L &= \frac{39168}{25} \text{lb} \quad \text{ or } \quad 1566.72 \text{lb}
\end{aligned}
\end{equation}
$

If the Area of the wing is $600 \text{ft}^2$ and the speed is $\displaystyle 40 \frac{\text{mi}}{\text{h}}$, then the lift will be $1566.72\text{lb}$

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