Chapter 8.9, Problem 15WE

To determine

To find: the approximate altitude.

Answer to Problem 15WE

The approximate altitude is $2070$ .

Explanation of Solution

Given information:

The air density is $1.000\frac{\text{kg}}{{\text{m}}^3}$ .

Calculation: let altitude is $x$ ,

Altitude	Density
$2000$	$1.007$
$x$	$1.000$
$2500$	$0.957$

Now, the difference,

  $\begin{array}{l}\frac{c}{500}=\frac{0.007}{0.05}\\ \frac{c}{500}=.14\text{ [divide]}\\ c\approx 70\text{ [multiply]}\end{array}$

Now, to find the value of altitude,

  $\begin{array}{l}x=2000+c\\ x=2000+70\text{ [substitute]}\\ x=2070\text{ [add]}\end{array}$

Thus, The value of altitude is $2070$ .