A buoy in the harbor of San Juan, Puerto Rico, bobs up and down. The distance between the highest and lowest point is 3 feet. It moves from its highest point down to its lowest point and back to its highest point every 8 seconds.
a. Find the equation of the motion for the buoy assuming that it is at its equilibrium point at t = 0 and the buoy is on its way down at that time.
b. Determine the height of the buoy at 3 seconds.
c. Determine the height of the buoy at 12 seconds.