To find the wind chill using the given formula, we substitute $V = 15$ mph and $T = 10$ degrees Fahrenheit into the equation:

$W(V, T) = 91.4 - \frac{(10.45 + 6.69 \sqrt{V} - 0.447 V)(91.4 - T)}{22}$

Step 1: Calculate $\sqrt{V}$

$\sqrt{15} \approx 3.873$

Step 2: Calculate the expression inside the parentheses

$10.45 + 6.69 \times 3.873 - 0.447 \times 15$ $= 10.45 + 25.91937 - 6.705$ $= 29.66437$

Step 3: Substitute and calculate the entire expression

Now substitute into the formula: $W(15, 10) = 91.4 - \frac{29.66437 \times (91.4 - 10)}{22}$

Step 4: Calculate $91.4 - 10$

$91.4 - 10 = 81.4$

Step 5: Multiply and divide

$29.66437 \times 81.4 \approx 2415.542818$ $\frac{2415.542818}{22} \approx 109.7974$

Step 6: Final subtraction

$W(15, 10) = 91.4 - 109.7974 \approx -18.397$

Thus, the wind chill is approximately -18.397 degrees Fahrenheit.

Would you like more details on any part of the calculation?

Related Questions:

1. How does the Wind Chill Index formula change for wind speeds below 4 mph?
2. Can you derive the wind chill for a wind speed of 30 mph and 0 degrees Fahrenheit?
3. What does each term in the Wind Chill Index formula represent physically?
4. How accurate is the Wind Chill Index for predicting frostbite risk?
5. Can this formula be applied to temperatures in Celsius, and if so, how would it be adapted?

Tip: Always round to at least three decimal places for precision in meteorological calculations.