The paddle wheel of a steamboat is 22 feet in diameter and is turning at a rate of 3 revolutions every two minutes. The axle of the wheel is 8 feet above the surface of the water. Locate the origin on your diagram so that a point P on the top edge of the paddle wheel is at (0,19) at time t=0 seconds.
A. What maximum height above the water does point P reach?
B. How far below the water does point P reach?
C. In how many seconds does the wheel complete one revolution?
D. Write a cosine function for the height of point, P at the time t.
E. Write a sine function for the height of point, P at time t.
F. Use the function from part d or e to find the time(s) at which point P will be at height 10 feet.