Chapter 3.4, Problem 24ES

An aircraft is flying horizontally at a constant height of $4000\text{ ft}$ above a fixed observation point (see the accompanying figure on the next page). At a certain instant the angle of elevation $\theta$ is $30°$ and decreasing, and the speed of the aircraft is $300\text{ mi/h}$ .

(a) How fast is $\theta$ decreasing at this instant? Express the result in units of deg/s.

(b) How fast is the distance between the aircraft and the observation point changing at this instant? Express the result in units of ft/s. Use $1\text{ mi}=5280\text{ ft}$ .