Answer:
<u><em>note:</em></u>
<u><em>solution is attached due to error in mathematical equation. please find the attachment</em></u>
I need help with this question ASAP please :)
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Answer:
The air temperature at the tropopause is - 79 °C
Explanation:
We know that a station near the equator has a surface temperature of 25°C
Vertical soundings reveal an environmental lapse rate of 6.5 °C per kilometer.
The tropopause is encountered at 16 km.
In order to find the air temperature at the tropopause we are going to deduce a linear function for the temperature at the tropopause.
This linear function will have the following structure :
Where '''' and ''
'' are real numbers.
Let's write to denote the temperature '' T '' in function of the distance
'' x '' ⇒
We can reorder the function as :
(I)
Now, at the surface the value of '''' is 0 km and the temperature is 25°C so in the function (I) we write :
⇒
⇒
(II)
In (II) the value of '''' represents the change in temperature per kilometer.
Because the temperature decrease with the height this number will be negative and also a data from the question ⇒
(III)
In (III) we deduced the linear equation. The last step is to replace by in (III) ⇒
The air temperature at the tropopause is - 79 °C
Recall that the dot product between two vectors and
satisfies
where denotes the norm of a vector
, and
is the angle between the two vectors.
So if and
, then