Chapter 2.6, Problem 69ES

The accompanying figure shows the graph of atmospheric pressure $p\left({\text{lb/in}}^2\right)$ versus the altitude $h\left(\text{mi}\right)$ above sea level.

(a) From the graph and the tangent line at $h=2$ shown on the graph, estimate the values of $p$ and $dp/dh$ at an altitude of $2\text{ mi}$ .

(b) If the altitude of a space vehicle is increasing at the rate of $0.3\text{ mi/s}$ at the instant when it is $2\text{ mi}$ above sea level, how fast is the pressure changing with time at this instant?