A security camera is centered 50 feet above a 100-foot hallway.

A security camera is centered 50 feet above a 100-foot hallway. It is easiest to design the camera with a constant angular rate of rotation, but this results in a variable rate at which the images of the surveillance area are recorded. So, it is desirable to design a system with a variable rate of rotation and a constant rate of movement of the scanning beam along the hallway. Find a model for the variable rate of rotation if |dx/dt| = 2 feet per second.