In a free-fall experiment, an object is dropped from a height of 256 feet. A camera on the ground 500 feet from the point of impact records the fall of the object (see figure).

(a) Find the position function that yields the height of the object at time t, assuming the object is released at time t = 0. At what time will the object reach ground level?

(b) Find the rates of change of the angle of elevation of the
camera when t = 1 and t = 2.

500 ft 256 ft Not drawn to scale