QuestionMay 3, 2025

5. What is the equivalent chill temperature for con ditions where the ambient temperature is 10^circ F and the wind speed is 20 mph?

5. What is the equivalent chill temperature for con ditions where the ambient temperature is 10^circ F and the wind speed is 20 mph?
5. What is the equivalent chill temperature for con ditions where the ambient temperature is 10^circ F and the wind speed is 20 mph?

Solution
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Answer

-12.87^{\circ}F Explanation 1. Use the wind chill temperature formula The wind chill temperature (T_w) is calculated using the formula: T_w = 35.74 + 0.6215T_a - 35.75v^{0.16} + 0.4275T_a v^{0.16}, where T_a is the ambient temperature in °F and v is the wind speed in mph. 2. Substitute the given values Substituting T_a = 10 and v = 20: T_w = 35.74 + 0.6215(10) - 35.75(20^{0.16}) + 0.4275(10)(20^{0.16}). 3. Simplify the terms Compute 20^{0.16} \approx 1.741: T_w = 35.74 + 6.215 - 35.75(1.741) + 0.4275(10)(1.741). T_w = 35.74 + 6.215 - 62.26 + 7.44. 4. Final calculation Combine all terms: T_w = -12.865.

Explanation

1. Use the wind chill temperature formula<br /> The wind chill temperature ($T_w$) is calculated using the formula: <br />$T_w = 35.74 + 0.6215T_a - 35.75v^{0.16} + 0.4275T_a v^{0.16}$, <br />where $T_a$ is the ambient temperature in °F and $v$ is the wind speed in mph.<br /><br />2. Substitute the given values<br /> Substituting $T_a = 10$ and $v = 20$: <br />$T_w = 35.74 + 0.6215(10) - 35.75(20^{0.16}) + 0.4275(10)(20^{0.16})$. <br /><br />3. Simplify the terms<br /> Compute $20^{0.16} \approx 1.741$: <br />$T_w = 35.74 + 6.215 - 35.75(1.741) + 0.4275(10)(1.741)$. <br />$T_w = 35.74 + 6.215 - 62.26 + 7.44$. <br /><br />4. Final calculation<br /> Combine all terms: <br />$T_w = -12.865$.
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