Chapter 3.3, Problem 44E

Related Rates An airplane flying $390$ feet per second at an altitude of $5000$ feet flew directly over an observer. Figure 8 shows the relationship of the airplane to the observer at a later time.

a. Find an equation relating $x$ and $y$.

b. Find the values of $x$ when $y$ is $13,000$.

c. How fast is the distance from the observer to the airplane changing at the time when the airplane is $13,000$ feet from the observer? That is, what is $\frac{dy}{dt}$ at the time when $\frac{dx}{dt}=390$ and $y=13,000$?