1. Ferris Wheel Comparison

2. World’s Fair Ferris Wheel.
Given info:
diameter 250ft , height from the ground 14ft, 1 period = 10 minutes.
h - vertical position (height) at time t where t is given in minutes
What are the five critical t-axis values ???
t (min)
h (ft) 14
2.5
139 5
264
7.5 10
250 ft
14 ft

3. Characteristics of the World’s Fair Ferris Wheel
Ride procedure: board the Ferris wheel at the bottom, height of 14 feet, go up, reach maximum after 5 minutes, complete one ride (one period) after 10 minutes.
This does not resemble parent graph of sin(x) or cos(x), we must apply a phase shift in the equation
Characteristics of the periodic function:
a) Phase shift: (sine), -  (cosine)
b) Vertical shift :
c) Amplitude: 125 ft
d) Period : 10 minutes  2/10 = 1/5  or 36
e) y-intercept: (0, 14)
f) Min. value: 14 ft Max. value: 264 ft
g) the height at time = 0 ? h(0) = 14

4. EQUATIONS Cosine equation for this ride: Sine equation for this ride:

5. GRAPHS: Cosine Equation
If the equation is written in radian measure, calculator mode must be in radian and the window settings must be appropriate:
X Min: 0
X Max: 10
Y Min: 0
Y Max: 300
Maximum
h(5)=264
a = 125 ft
Minimum h(0)= 14 h(10)=14

6. GRAPHS: Sine Equation(s)
Maximum
h(5)=264
Maximum
h(180)=264
a = 125 ft
a = 125 ft
Minimum h(0)= 14 h(10)=14

7. Calculations for World’s Fair Ferris Wheel
1)What is the circumference of the wheel? C = 250 ft
2.) At what speed is the wheel traveling? Speed = 1.31 ft/sec.
If you begin your ride at the base of the wheel, what is your height after minute? h(1) = ft
4 minutes? h(4) = ft
At what approximate time(s) will you reach the following heights?
a.) 100 ft t(100) 2 min AND t(100) 8 min
b.) 240 ft. t(240) 4 min AND t(240) 6 min

8. Navy Pier Ferris Wheel. Given info:
diameter 140ft , height from the ground 10ft, 1 period = 6 min
h - vertical position (height) at time t where t is given in minutes
What are the five critical t-axis values ???
t (min)
h (ft) 10
1.5 80 3
150
4.5 6
140 ft
10 ft

9. Characteristics of the Navy Pier Ferris Wheel
Ride procedure: board the Ferris wheel at the bottom, height of 10 feet, go up, reach maximum after 3 minutes, complete one ride (one period) after 6 minutes.
This does not resemble parent graph of sin(x) or cos(x), we must apply a phase shift in the equation
Characteristics of the periodic function:
a) Phase shift: (sine), -  (cosine)
b) Vertical shift : +80
c) Amplitude: 70 ft
d) Period : 6 minutes  2/6 = 1/3  or 60
e) y-intercept: (0, 10)
f) Min. value: 10 ft Max. value: 150 ft
g) the height at time = 0 ? h(0) = 10

10. EQUATIONS Cosine equation for Navy Pier ride:

11. GRAPHS: Maximum h(3)=150 Maximum h(3)=150 a = 70 ft a = 70 ft
Minimum h(0)= 10 h(10)=10

12. Calculations for Navy Pier Ferris Wheel
1)What is the circumference of the wheel? C = 140 ft
2.) At what speed is the wheel traveling? Speed = 1.2 ft/sec.
If you begin your ride at the base of the wheel, what is your height after minute? h(1) = 45 ft
4 minutes? h(4) = 115 ft
At what approximate time(s) will you reach the following heights?
a.) 100 ft t(100) 4.2 min AND t(100)7.8 min
b.) 240 ft. t(240) NEVER

13. Ferris Wheel Challenge
World’s Fair Ferris Wheel and Navy Pier Ferris Wheel ride over 20 minutes
Imagine the Navy Pier
and the Worlds Fair
Ferris Wheel being built
beside each other. If
both wheels begin
turning at once, over a
20 minute time period, at
what times are the
wheels at the same height?
h(2.5)=141.95
h(7.9)=108.2
h(18.9)=40.95
h(11.1)=40.95
h(0.6)=21.6

14. Ferris Wheel Challenge
What is the length of the arc traveled by the Navy Pier Ferris wheel from the 4 o’clock to the 7 o’clock position?
Circumference = 140 ft
From 4 o’clock  7 o’clock = 3 hours = 90 = /2  ¼ of the circumference
Arc length = ( ¼ ) (140) = ft