# Webquest case study on roller coasters and theme parks

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Lesson 1 - 3
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The following exercise must be completed and submitted to your instructor for grading. Click here for directions on how to submit your assignment.
Introduction
What's your favorite ride at the Amusement Park? Maybe it’s the Merry-Go-Round or perhaps the waterslide or bumper cars. Do you like roller coasters? Most teenagers love the thrill of roller coasters!
When the coaster is released at the top of the first hill, gravity takes over. Gravity applies a constant downward force on the cars. The coaster tracks serve to channel this force - they control the way the coaster cars fall. If the tracks slope down, gravity pulls the front of the car toward the ground, which makes it accelerate. If the tracks tilt up, gravity applies a downward force on the back of the coaster, causing it to decelerate. When the coaster ascends, one of the smaller hills that follow the initial lift hill makes the kinetic energy change back to potential energy. In this way, the course of the track is constantly converting energy from kinetic to potential and back again. This fluctuation in acceleration is what makes roller coasters so much fun.
In this project, called a Web Quest, you will dive into the World of Roller Coasters. You will learn about the history of coasters and research some found in the United States. Most importantly, you will use some of the mathematical skills you have just learned to help you better understand how roller coasters work.
Some of the fundamental properties that make roller coasters work, including hills and dips, acceleration, loops and centripetal force can be explained using mathematical models. Roller coasters are driven almost entirely by basic inertial, gravitational and centripetal forces. All of this is manipulated in order to create a great ride. Amusement parks keep building faster and more complex roller coasters, but the fundamental principles at work remain the same.
A roller coaster's energy is constantly changing between potential and kinetic energy. At the top of a first lift hill, there is maximum potential energy because the train is as high as it gets. As the train starts down the hill, this potential energy is converted into kinetic energy, so the train speeds up. At the bottom of a hill, there is maximum kinetic energy and little potential energy. The kinetic energy propels the train up the second hill, building up the potential-energy level. As the train enters a loop, it has a lot of kinetic energy and not much potential energy. The potential-energy level builds as the train speeds to the top of the loop, but it is soon converted back to kinetic energy as the train leaves the loop.
You are part of a team that is studying how mathematics and science influence how roller coasters work. You have been charged with making some mathematical justifications and explanations for the elementary physics behind roller coaster motion. You will use your knowledge to make a recommendation for safe, yet fun roller coasters.
To complete this task, you must research the following questions:
• Historically speaking, what makes roller coasters so popular?
• How has roller coaster design evolved since the original coasters?
• What are some of the theme parks in the United States that have roller coasters? What are the popular roller coasters at these sites?
• What are the safety considerations when designing a roller coaster?
• What is the distance, rate of speed and time duration for different roller coasters?
• What is acceleration and how does it relate to roller coaster thrills?
The Process
1. Find the locations of at least three early roller coasters in the United States. Who were the designers? What material was used to build the coasters? Are those same materials used today? If not, what other materials are used?
2. Select five theme parks. Begin to complete the data collection sheet for five roller coasters at parks near your home or ones you have visited.
3. Calculate the time duration of the roller coaster rides. Use the formula d=rt. Here d is distance or length of coaster. The variable r is rate or speed and t is time. Be careful with your unit conversions. Remember that 1.0 meter = 3.281 feet and 1 mile = 5280 feet. Add this data to your data collection sheet.
4. Calculate the average acceleration for the roller coasters you selected. The formula for finding average acceleration is: s=(vo)t + 1/2at2. Where s (Distance in meters - 1.0 meter = 3.281 feet) is equal to vo (Initial Velocity - for coasters this is zero) multiplied by t (time in seconds) plus one-half a (Average Acceleration - what we are looking for) multiplied by t squared (time in seconds again). Add this data to your data collection sheet.
5. Complete three simulated roller coaster trials to determine combinations of factors that are useful for both safe and fun coasters. Go to the website http://www.learner.org/exhibits/parkphysics/coaster/ to perform the simulations. Write a detailed description of what you do at the website. This question is worth 20 points.
Name of Theme Park Location in U.S. Name of Roller Coaster Height Length Speed (rate) Duration of ride (time) Average acceleration

Height of the 1st Hill Shape of the 1st Hill The Exit Path Height of the 2nd Hill The Loop Results
Trial 1
Trial 2
Trial 3

Web Resources
History of Roller Coasters
http://www.ultimaterollercoaster.com/coasters/history/
http://search.eb.com/coasters/
Roller Coaster Terminology
http://www.ultimaterollercoaster.com/coasters/glossary/
http://web.archive.org/web/20070203165930/http://www.cinternet.net/~bowersda/coasters.htm
Roller Coaster Locator
http://www.coaster-count.com/world.xhtml
http://web.archive.org/web/20070203142839/http://www.cinternet.net/~bowersda/glossary.htm
http://www.sixflags.com/pick_a_park1.asp
Ask a scientist and other basic physics
http://howthingswork.virginia.edu/
http://hyperphysics.phy-astr.gsu.edu/hbase/cf.html
http://www.phy.ntnu.edu.tw/java/circularMotion/circular3D_e.html
http://www.phys.virginia.edu/classes/605.ral5q.fall02/lectures/carousels_and_roller_coasters.pdf
Roller Coaster Statistics
http://www.sixflags.com/
http://www.rcdb.com/
http://www.learner.org/exhibits/parkphysics/coaster.html
Create simulation
http://www.learner.org/exhibits/parkphysics/coaster/
Conclusions
Prepare a report of your findings, which should include your data sheet and an explanation of which roller coaster is the safest and most fun. If you can create a table to display your information, please do so. Otherwise, just list the answers with its corresponding heading. Use the data and results of your simulations to support your claim. Additionally, answer the questions mentioned earlier:
• Historically speaking, what makes roller coasters so popular?
• How has roller coaster design evolved since the original coasters?
• What are some of the theme parks in the United States that have roller coasters? What are the popular roller coasters at these sites?
• What are the safety considerations when designing a roller coaster?
• What is the distance, rate of speed and time duration for different roller coasters?
• Please find 2 more roller coaster's length, time duration and its rate of speed. DO NOT repeat the same roller coasters mentioned in the chart in Question 2 of the process for this question.
• What is acceleration and how does it relate to roller coaster thrills?

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Lesson 4 - 6
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Lesson 4 - 6
The following exercise must be completed and submitted to your instructor for grading. Click here for directions on how to submit your assignment.
Introduction
Suppose you received \$10,000 to invest in theme parks by buying stocks from the New York Stock Exchange (NYSE) or Mutual Funds. You will select three theme parks. You are also required to keep the stocks for a while and then sell them. You will find out if you made a profit or lost money.
I hope that you use this information to further your knowledge of investment matters and continue your interests in making the right decision to ensure your financial future when the occasion arises.
Research three different theme parks and select the theme park you believe will make you the most profit. After you decide on a theme park, buy \$10,000 worth of its stock from NYSE or Mutual Funds, and then sell after four weeks. Record your data and generate graphs to illustrate your research. Calculate the profit made or lost from the stock. Compare this to investing the same amount of money in a savings account.
The Process
1. Choose three theme parks that have stocks on the NYSE or Mutual Funds. Go to http://finance.yahoo.com/education/stocks and click on “How the Stock Market Works” to learn about stocks. To find a public traded theme park stock, search on google (http://google.com) with these words "publicly traded theme park stock". It should produce at least two theme parks that are traded on the stock market. You may have to find out if the company is traded on the stock market by looking up the parent company that owns the theme park.
2. Check the financial history of the theme parks you selected for the past five years at http://finance.yahoo.com/. Use the resources to help you find the following information:
a. Determine which theme park was most profitable over the last year. Determine which theme park was most profitable over the past five years. Record your findings.
b. Which theme park will provide you with the most profit or the least amount of loss? Select a theme park you feel will be most profitable and discuss why.
c. Buy \$10,000 worth of the theme park shares in stocks or mutual funds.
d. Use the following formula to calculate the number of shares, including a 2% broker’s fee:
# of shares = 10000/ (1.02 • initial price per share)
3. Record the stock’s price over a period of four weeks. Use the OPEN price for each day using http://finance.yahoo.com/. Generate a line graph. Cut and paste a line graph from yahoo finance OR make one of your own.
4. Calculate the net profit or net loss for each stock, including a 2% broker’s fee. Use this formula:
Selling cost = Price per share • # of shares • 2%
Net Sales = (price /share) • (# of shares) - selling cost
Profit /Loss = Net Sales - \$10,000
To make a graph: In Excel, you will have to have a column for x which will be the dates of the stock prices and the y column is the stock's price. Highlight the two columns (x being on the left column and y being on the right of x. Go to Insert and then chart in the menu. You can use line or xy (scatter) to graph this information. Click okay and you have a graph in Excel.
Resources
The following are possible resources you can use to help in your web quest.
http://finance.yahoo.com/
http://nyse.com
http://morningstar.com
Conclusion
Write up your findings in a document that contains answers to all of the information asked in The Process section. Additionally, be sure to answer the questions below.
• What do you think your stock will be worth in five years?
• Compare your results to investing \$10,000 in a savings account that has an interest rate of 3.5% compounded annually for five years.
• If you kept your stocks for five years, which investment would provide you with the most profit: your theme park or the savings account?

Essay style solutions to the questions/lessons presented above!

Other Details about the Project/Assignment
Subjects: Statistics and General Research
Topic: Roller Coaster and Theme Parks
Level: College / University
Tags:

### Webquest

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Project Details
Subjects: Statistics and General Research
Topic: Roller Coaster and Theme Parks
Level: College / University
Tags:

## Webquest

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