A Ferris wheel has a 40-foot radius and the center of the Ferris wheel is 46 feet above the ground. The Ferris wheel in the CCW direction at a constant angular speed of 2 radians per unit minute. John boards the Ferris wheel at the 3 o’clock position and rides the Ferris wheel for many rotations. Let t represent the number of minutes since the ride started.

a. Write an expression (in terms of t) to represent the number of radians John has swept out from the 3 o’clock position since the ride started.

b. How long does it take for John to complete one full revolution (rotation)?

c. Write an expression (in terms of t) to represent John’s height above the center of the Ferris wheel (in feet).

d. Write a function f that determine’s John’s height above the ground (in feet) in terms of t.