Ferris Wheel Comparison Project

The 1893 Chicago World’s Fair is considered the birthplace of the classic amusement park ride, the Ferris wheel. The architectural wonder was created by an American engineer named George Ferris. The original Ferris wheel no longer exists. But, in 1990, a new Ferris wheel was built at Navy Pier in Chicago to resemble the original. While the Navy Pier Ferris Wheel is a beautiful Chicago landmark, its grandeur actually pales in comparison to Mr. Ferris’ creation.

The Ferris wheel built for the World’s Fair had a diameter of 250 feet. It stood 14 feet off the ground. It had 36 wooden boxcars that were the size of train cars. Each car could hold 60 people! The wheel would load cars in such a way that each rider could enjoy a full rotation that lasted about 10 minutes.

The Ferris wheel at Navy Pier has a diameter of 140 feet. It stands 10 feet off the ground. The wheel has 40 gondolas that seat six passengers each. It takes about 6 minutes for the Navy Pier Ferris Wheel to complete one rotation.

Below is a picture of the first Ferris wheel next to the Ferris wheel at Navy Pier.

Ferris Wheel Comparison Name(s) ___________________________________________In the space below is a diagram of the World’s Fair

Ferris wheel and the boarding platform. Fill in the

necessary information.

Now, complete the table below. Let h represent your

vertical position (height) at time t where t is given in

minutes. Remember, you need 5 critical t-axis values.

t h

Before you sketch the cosine and sine graphs, answer each of the following.

1.) What is the amplitude of the graph? a = __________

2.) What is the period of your curve? b = __________

3.) What are your 5 critical t-values? _________________________________

4.) What are the maximum and minimum values Max ________ Min ________ of your curve?

5.) What is the height at time = 0 (y-intercept)? ______________

Write a cosine equation for your curve.

_____________________________________

Graph the equation.

Write a sine equation for your curve.

__________________________________

Graph the equation.

1.) What is the circumference of the wheel?

2.) At what speed is the wheel traveling? Please give your answer in feet/second.

3.) If you begin your ride at the base of the wheel, what is your height after 1 minute? _____ 4 minutes? _____

4.) At what approximate time(s) will you reach 100 ft.? _____ 240 ft.? _____

h =

d =

In the space below is a diagram of the Navy Pier Fair

Ferris Wheel and the boarding platform. Fill in the

necessary information.

Now, complete the table below. Let h represent your

vertical position (height) at time t where t is given in

minutes. Remember, you need 5 critical t-axis values.

t h

Before you sketch the cosine and sine graphs, answer each of the following.

1.) What is the amplitude of the graph? a = __________

2.) What is the period of your curve? b = __________

3.) What are your 5 critical t-values? _________________________________

4.) What are the maximum and minimum values Max ________ Min ________ of your curve?

5.) What is the height at time = 0 (y-intercept)? ______________

Write a cosine equation for your curve.

_____________________________________

Graph the equation.

Write a sine equation for your curve.

__________________________________

Graph the equation.

1.) What is the circumference of the wheel?

2.) At what speed is the wheel traveling? Please give your answer in feet/second.

3.) If you begin your ride at the base of the wheel, what is your height after 1 minute? _____ 4 minutes? _____

4.) At what approximate time(s) will you reach 100 ft.? _____ 240 ft.? _____

h =

d =

Now to compare… Imagine the World’s Fair Ferris Wheel and the Navy Pier Ferris Wheel were built side by

side. If both wheels begin turning at the same time, over a 20 minute time period, at what times are the wheels

at the same height?