Answer
The wind speed to the nearest mile per hour is 18 mi/h.
Work Step by Step
The formula for WCT if the wind speed is above 3 mi/h is:
$WCT = 35.74 +0.6215T - 35.75v^{0.16} + 0.4275Tv^{0.16}$
Where WCT is the equivalent temperature in °F, T is the outside or air temperature in °F, and v is the wind speed.
In the question, WCT = 5 °F, T = 20 °F, and v is unknown. Thus, replacing the values of the known parameters in the equation above, we have:
$5 = 35.74 +0.6215\times20 - 35.75v^{0.16} + 0.4275\times20v^{0.16}$
$5 = 35.74 +12.43 - 35.75v^{0.16} + 8.55v^{0.16}$
Collecting like terms and rearranging, we have:
$-5 +35.74+12.43 = 35.75v^{0.16} - 8.55v^{0.16}$
$43.17 = 27.2v^{0.16}$
Dividing both sides by the 27.2, we have:
$\frac{43.17}{27.2} = \frac{27.2}{27.2}v^{0.16}$, $v^{0.16}$=1.587
$\sqrt[0.16] v^{0.16}=\sqrt[0.16] {1.587}$
$v = 17.94 $
The wind speed to the nearest mile per hour is 18 mi/h.
