In one scene of a movie, a man is tied to a water wheel. Assume the wheel has a diameter of 8 m and the center of the wheel is 3 m above the water. When you first notice the man on the wheel (which moves counterclockwise), the man is at the 3 o'clock position (as shown). Four seconds later, he is at 12 o'clock (the greatest height). a) Let h(t) represent the height of the man above the water t seconds after you first notice him. Sketch the graph of h(t). Be sure to clearly label the key points on your graph (max, min, midline).

b) Write an equation for h(t).

c) How long does the man spend under water with each revolution of the wheel? Show algebraic solving work to support your answer.