Dr. Paul Siple conducted studies testing the effect of wind on the formation of ice at various temperatures and developed the concept of wind chill, which we hear reported during winter weather reports. In 2001, the National Weather Service introduced the new wind chill index given in the table. This new index is more accurate at measuring how cold it feels when it is windy. For example, the table shows that an air temperature of 15ºF together with a wind speed of 35 mph feels the same as an air temperature of -7ºF when there is no wind.

The wind chill WC has been modeled by WC = 35.74 + 0.6215t - 35.75s^0.16 + 0.4275ts^0.16 where s is the wind speed and t actual air temperature. Use this model to answer Problems

(a) To see how wind chill temperature changes with temperature, find ∂WC/∂t.

(b) Find ∂WC/∂t when the temperature is 10°F and the wind speed is 25 mph. What does this mean?

Transcribed Image Text:

Air Temperature (°F) 35 25 15 5 -5 -15 -25 31 19 7 -5 -16 - 28 -40 15 25 13 -13 -26 -39 -51 25 23 9. -4 -17 -31 -44 -58 35 21 7 -7 -21 -34 -48 -62 45 19 -9 - 23 -37 -51 -65 Wind Speed (mph)