A camera is tracking the launch of a SpaceX rocket. The camera is located \(4000\)’ from the rocket’s launching pad, and the camera angle changes in order to keep the rocket in focus. At what angle \(\theta\) (in radians) is the camera tilted when the rocket is \(3000\)’ off the ground? Answer both exactly and approximately.

Now, rather than considering the rocket at a fixed height of \(3000\)’, let its height vary and call the rocket’s height \(h\text{.}\) Determine the camera’s angle, \(\theta\) as a function of \(h\text{,}\) and compute the average rate of change of \(\theta\) on the intervals \([3000,3500]\text{,}\) \([5000,5500]\text{,}\) and \([7000,7500]\text{.}\) What do you observe about how the camera angle is changing?