Question

The wind chill factor represents the equivalent air temperature at a standard wind speed that would produce the same heat loss as the given temperature and wind speed. One formula for computing the equivalent temperature is

𝑡
W(t) = {33 − (10.45+10√𝑣−𝑣)(33−𝑡) / 2204
33 − 1.5958(33 − 𝑡)

if 0 ≤ v < 1.79
if 1.79 ≤ v < 20
if v ≥ 20

where v represents the wind speed (in meters per second) and t represents the air temperature . Compute the wind chill for an air temperature of 15°C and a wind speed of 12 meters per second. (Round the answer to one decimal place.) Show your work.

Answer 1

[AI-generated answer — Explain Bot]

To compute the wind chill for an air temperature of 15°C and a wind speed of 12 meters per second, we need to use the wind chill formula and substitute the given values.

Given:
Temperature (t) = 15°C
Wind Speed (v) = 12 m/s

First, let's determine the range of wind speed that applies to our given value of v. In this case, 1.79 ≤ 12 < 20, so we use the second part of the formula.

Now, we can substitute the values into the formula:

W(t) = {33 − [(10.45+10√v−v)/(33−t)]} / [33 − 1.5958(33 − t)]

W(t) = {33 − [(10.45+10√12−12)/(33−15)]} / [33 − 1.5958(33 − 15)]

Next, let's simplify the formula step by step:

W(t) = {33 − [(10.45+10√12−12)/18]} / [33 − 1.5958(18)]

W(t) = {33 − [(10.45+10√12−12)/18]} / [33 − 28.8744]

Now, let's evaluate the numerator first:

Numerator = (10.45+10√12−12)

Numerator = 10.45 + 10√12 - 12

Numerator = 10.45 + 10(√12) - 12

Numerator = 10.45 + 10(3.464) - 12 (since √12 = 3.464)

Numerator = 10.45 + 34.64 - 12

Numerator = 43.09 - 12

Numerator = 31.09

Now, substitute this value back in the formula:

W(t) = {33 − (31.09/18)} / [33 − 28.8744]

W(t) = {33 - 1.7272} / 4.1256

W(t) = 31.2728 / 4.1256

W(t) ≈ 7.57°C

Therefore, the wind chill for an air temperature of 15°C and a wind speed of 12 meters per second is approximately 7.57°C.