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If you are outdoors, the wind may make it feel a lot colder than the thermometer reads

Chapter 3, Problem 56

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QUESTION:

If you are outdoors, the wind may make it feel a lot colder than the thermometer reads. You feel the windchill temperature, which, if the air temperature is \(20^{\circ} \mathrm{F}\), is given in \({ }^{\circ} \mathrm{F}\) by \(W(v)=48.17-27.2 v^{0.16}\), where v is the wind velocity in mph for \(5 \leq v \leq 60 .^{2}\)

(a) If the air temperature is \(20^{\circ} \mathrm{F}\), and the wind is blowing at 40 mph, what is the windchill temperature, to the nearest degree?

(b) Find \(W^{\prime}(40)\), and explain what this means in terms of windchill.

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QUESTION:

If you are outdoors, the wind may make it feel a lot colder than the thermometer reads. You feel the windchill temperature, which, if the air temperature is \(20^{\circ} \mathrm{F}\), is given in \({ }^{\circ} \mathrm{F}\) by \(W(v)=48.17-27.2 v^{0.16}\), where v is the wind velocity in mph for \(5 \leq v \leq 60 .^{2}\)

(a) If the air temperature is \(20^{\circ} \mathrm{F}\), and the wind is blowing at 40 mph, what is the windchill temperature, to the nearest degree?

(b) Find \(W^{\prime}(40)\), and explain what this means in terms of windchill.

ANSWER:

Step 1 of 3

(a)

We are given the equation \(W\left( v \right) = 48.17 - 27.2{v^{0.16}}\), where v is the wind velocity in mph when between \(5 \le v \le 60\). And W is the temperature in degrees Fahrenheit. For this part of the question, we are just required to plug 40 mph in for v.

\(W\left( {40} \right) = 48.17 - 27.2 \times {40^{0.16}}\)

\(W\left( {40} \right) =  - 0.909\)

\(W\left( {40} \right) =  - 1\;{\rm{degrees}}\;{\rm{Fahrenheit}}\)

Hence, the windchill temperature is determined as -1 degrees Fahrenheit.

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