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

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.




W(t) = {33-(10.45+10sqrtv-v)(33-t)/2204
33-1.5958(33-t)
if 0≤v<1.79
if 1.79≤v<20
if v≥20

Answer 1

The wind chill equations I have found are more complicated than that.

Answer 2

First of all we have to re write the equation like this:

`W(t)=\left \{ {{33-((10.45+10√(v)-v(33-t) )/(2204)if 0\leq v<1.79} \atop {33-1.5958(33-t)if 1.79\leq v<20 }} \right.`

To solve this problem we have to replace the values (
`t=15` and
`v=12`) in the previous equation, as we can see in the limits of the equation the value given for v would fit in the second condition (
`1.79\leq 12<20`) so we would use the second part of the equation like this:

`W(t)=33-1.5958(33-t)\\W(15)=33-1.5958(33-(15))=33-1.59589(18)=33-28.7244=4.2756`

and rounding to one decimal place (we round up because the next digit from the first decimal place is bigger than 5) :

`W(15)=4.3`