Ferris wheel
Function
To celebrate the new millennium, the British planned to construct the world’s largest Ferris wheel. The
London Eye or “Millennium Wheel” is located in London, England, and measures approximately 500 ft. It
turns continuously and completes a single rotation every 30 minutes. They wanted it to be slow enough
for people to hop on and off while it rotates.
1. Assume the wheel is turning counterclockwise and your height above the ground, h(t) in feet, is a
function of t, the number of minutes you have been riding. You decide to ride the Ferris wheel for 3 full
turns, and you hop on at time t=0 at the 6 o’clock position.
t
0
h(t) 0
7.5
15
22.5 30
37.5 45
52.5 60
67.5 75
82.5 90
2. Graph the data from the table:
500
250
3. Should the points on the graph above be connected by straight lines? Describe the shape of the graph.
4. A function f is periodic if its values repeat on regular intervals. Graphically, this means that if the graph
of f is shifted horizontally by c units, for some constant c, the new graph is identical to the original. Thus,
f (t  c)  f (t) for all t in the domain of f. The smallest value of c for which this relationship holds for all
values of t is called the period of f.
What is the period of the Ferris wheel function?___________________________

5. The midline of a trigonometric function is the horizontal line midway between the function’s maximum
and minimum values. The amplitude is the distance between the function’s maximum (or minimum)
value and the midline.
Sketch a dotted line as the midline on the graph of h(t). What is the amplitude of h(t)?______
6. On a separate sheet of paper, sketch a graph of h(t), your height in feet above the ground t minutes
after you board the wheel. Label the period and amplitude of each graph as well as both axes. For all
problems, first determine an appropriate interval for t, with t  0. Also, identify the domain and range of
each graph.
A. The London Eye wheel has increased its rotation speed. The wheel begins to turn in a
counterclockwise direction completing one full 
revolution every 10 minutes. You ride for 2 complete
revolutions.
Period:_______________
Amplitude:___________
Domain:______________
Range:________________
B. Assume that everything is the same as A above except that the wheel turns in a clockwise direction.
Period:_______________
Amplitude:___________
Domain:______________
Range:________________
C. Assume that everything is the same as A except the developers decide to build the wheel with a 600
feet diameter.
Period:_______________
Amplitude:___________
Domain:______________
Range:________________
D. A new wheel is designed that is 20 meters in diameter and must be boarded from a platform that is 4
meters above the ground. Assume the 6 o’clock position on the Ferris wheel is level with the loading
platform. The wheel turns in the clockwise direction, completing one full revolution every 2 minutes.
Suppose at t  0 you are in the 12 o’clock position. From time t  0 you will make 2 complete
revolutions and then any additional part of a revolution needed to return to the boarding platform.
Period:_______________

Amplitude:___________
Domain:______________

Range:________________
7. The table below gives the height in feet of a weight suspended on a spring as it moves vertically as a
function of time in seconds. Find the appropriate amplitude and period of the function h  f (t) .
t
f (t)
0
4
1
2
3
4
5
6 7
8
9
10
11
12 13
14
15
5.25 6.165 6.5 6.167 5.25 4 2.75 1.835 1.5 1.8348 2.75 4 5.22 6.16 6.5

Period:_______________
Amplitude:___________