Questions: The force F on the blade of a wind generator varies jointly as the blade area A and the square of the wind velocity v. Find the equation relating F, A, and v if F=19.6 lb when A=3.76 ft^2 and v=31.7 ft / s. Choose the correct answer below. A. 0.00519 A v^2 B. 0.005187 Av^2 C. 0.005 Av^2 D. 0.0052 Av^2

Solution Steps

The problem states that the force $F$ varies jointly as the blade area $A$ and the square of the wind velocity $v$. This means we can express the relationship as: $$F = k \cdot A \cdot v^2$$ where $k$ is the constant of proportionality.

We are given that $F = 19.6 \, \text{lb}$, $A = 3.76 \, \text{ft}^2$, and $v = 31.7 \, \text{ft/s}$. Substitute these values into the equation to solve for $k$: $$19.6 = k \cdot 3.76 \cdot (31.7)^2$$

First, calculate $(31.7)^2$: $$(31.7)^2 = 1004.89$$

Now substitute back into the equation: $$19.6 = k \cdot 3.76 \cdot 1004.89$$

Solve for $k$: $$k = \frac{19.6}{3.76 \cdot 1004.89}$$

Calculate the denominator: $$3.76 \cdot 1004.89 = 3778.4064$$

Now calculate $k$: $$k = \frac{19.6}{3778.4064} \approx 0.005187$$

Substitute $k$ back into the original equation: $$F = 0.005187 \cdot A \cdot v^2$$

Final Answer