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The problem involves calculating the wind chill factor \( W \), which represents the air temperature at a standard wind speed that would produce the same heat loss as the given temperature and wind speed.

The provided formula for \( W \) depends on wind speed \( v \) (in meters per second) and air temperature \( t \) (in degrees Celsius). It is divided into three cases based on the value of \( v \):

\[
W = 
\begin{cases} 
t & 0 \leq v < 1.79 \\
32 - \frac{(10.43 + 10\sqrt{v} - v)(32 - t)}{22.04} & 1.79 \leq v \leq 25 \\
32 - 1.5958(32 - t) & v > 25
\end{cases}
\]

We are asked to find the wind chill factor for an air temperature of \( 5^\circ C \) and a wind speed of \( 1 \, \text{m/s} \).

### Step 1: Identify which case applies
The wind speed \( v = 1 \, \text{m/s} \) falls under the first case, where \( 0 \leq v < 1.79 \). In this case, the wind chill \( W \) is equal to the air temperature:

\[
W = t
\]

### Step 2: Plug in the air temperature
Given that \( t = 5^\circ C \), we simply substitute \( t \) into the equation:

\[
W = 5^\circ C
\]

Thus, the wind chill factor for this case is approximately \( 5^\circ C \).

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Would you like any additional details or have any questions about this solution? Here are 5 related questions for further exploration:

1. How would the wind chill change if the wind speed increased to 2 m/s?
2. What happens to the wind chill when the wind speed exceeds 25 m/s?
3. How does the wind chill formula account for the effects of wind speed on temperature?
4. Can wind chill ever be higher than the actual air temperature?
5. What are some real-world implications of the wind chill effect in outdoor environments?

**Tip**: Wind chill describes how cold it feels, not the actual temperature—always dress warmer than the air temperature when strong winds are present!

Find the wind chill for an air temperature of 5°C and a wind speed of 1 m/s.

Calculate the wind chill for an air temperature of 5°C and a wind speed of 1 m/s. This problem introduces the wind chill formula and its piecewise function, with detailed steps for determining the temperature effect based on wind speed.

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