Chapter 3 - Polynomial and Rational Functions - 3.6 Variation - 3.6 Exercises - Page 389: 41

$800\ lb$

Step 1. Assume $F\ (lb)$ is the force of the wind blowing on a vertical surface. Step 2. Assume $A\ (ft^2)$ is the area of the surface and $v\ (mph)$ is the velocity. Step 3. From the given conditions, we have $F=kAv^2$ and $50=k(\frac{1}{2})(40)^2$, thus $k=0.0625$ Step 4. For $v=80\ (mph)$ and $A=2\ (ft^2)$, we have $F=kAv^2=0.0625(2)(80)^2=800\ lb$