Chapter 4.7, Problem 109PE

A video camera located at ground level follows the liftoff of an Atlas $V$ Rocket from the Kennedy Space Center. Suppose that the camera is $1000\text{ m}$ from the launch pad.

a. Write the angle of elevation $\theta$ from the camera to the rocket as a function of the rocket's height $h$ .

b. Without the use of a calculator, will the angle of elevation be less than $45°$ or greater than $45°$ when the rocket is $400\text{ m}$ high?

c. Use a calculator to find $\theta$ to the nearest tenth of a degree when the rocket's height is $400\text{ m},1500\text{ m}$ , and $3000\text{ m}$ .