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