Building the Best Roller Coaster

Introduction | Task | Process | Guidance | Conclusion | Questions

Introduction
     Each year, amusement park owners compete to earn part of the billions of dollars Americans spend at amusement parks. Often the parks draw customers with new taller and faster roller coasters. In this project, you will explore how radical and rational functions are related to buying and building a new roller coaster.

The Task
You design roller coasters for a company that sells coasters to amusement parks all over the world. Your job also includes preparing a portfolio or Web page for prospective buyers that shows the roller coaster design, the speed of the coaster, and the cost of the coaster. You also need to include information about financing the cost of the coaster. You have just developed a new roller coaster and need to prepare a portfolio or Web page of materials for the buyers. Your portfolio or Web page must include the following information:

• a scale drawing of the new coaster you have designed;
• calculations showing the speed of your roller coaster at two locations during the ride;
• the cost of your roller coaster and two options for financing the cost of the roller coaster for the purchaser (this could include different interest rates, lengths of loans, and the amount of money used as a down payment);
• a table showing the payments and remaining balance for at least the first two years of payments on the coaster.

The Process
To successfully complete this project, you will need to complete the following items.

• Draw a scale diagram of your roller coaster.
• Find formulas to help you calculate the speed of a roller coaster at two locations during the ride. For help, try these Web sites.
  www.excite.com and search for roller coasters
  www.infoplease.com and search for roller coasters
  www.howstuffworks.com/link42.htm and search for roller coasters
  www.ultimaterollercoaster.com
  www.coasters.net/parks/cp.html
  
• Find formulas for helping you to present two options for financing the roller coaster. For help, try these Web sites.
  www.interest.com
  www.excite.com and search for interest calculators
  www.efunda.com/formulae/finance/loan_calculator.cfm
  
• Be creative. Add pictures or colorful illustrations to your portfolio or Web page.

Guidance
Here are some additional questions and ideas you may want to consider for your project.

1. How does changing the height or the length of a hill of a roller coaster affect the speed?
2. What types of skills does the designer of a roller coaster need? To find out, interview an engineer, or a designer of amusement park rides.
3. What physics principles are used in the design of roller coasters and other thrill rides? To find out, interview a physics teacher.
4. How does the rate of interest affect the payments that must be made on money that is borrowed? How does the length of time of the loan affect the total amount of interest paid when borrowing money?
5. How might you estimate the amount of money that can be generated by a roller coaster?

Conclusion
Here are some ideas for concluding your project.

• Present your project to your class or at a family night.
• Write a one-page summary of your project, including what you have learned from researching this topic.
• Make a poster for your project in addition to preparing a portfolio or Web page. Have other students critique the information presented on your poster.

Questions

Lesson 11–1
Maurice is preparing his calculations to show the speed of his new roller coaster at the top of one of the hills. Suppose the coaster reaches its maximum speed of 72 miles per hour at the bottom of the second hill, which is 157 feet tall. The formula for determining the speed of a coaster at the top of any hill is , where
v₁ = speed at the top of the hill in ft/sec,
v₂ = speed at the bottom of the hill in ft/sec,
h₁ = height at top of hill in feet,
h₂ = height at bottom of hill in feet, and
g = 32 ft/sec², the constant for gravity.
Assume that the bottom of the hill has height 0 ft.

1. What will be the value of 2gh₂? Why?
2. The value of v₂ in the formula should be expressed in ft/sec since the value of g is in ft/sec². What is the maximum speed of the coaster at the bottom of the hill in ft/sec?
3. List the values for each variable to use in the expression on the right side of the formula.
4. What is the speed of the coaster at the top of the second hill?

Lesson 12–2
Jada is preparing a portfolio for her roller coaster design. The cost of the roller coaster is $1,000,000. She assumes that an amusement park may want to make a down payment of $100,000. Then they will finance the remaining $900,000 for 30 years. The current rate of interest offered by a particular bank is 7.25%. She wants to know the monthly payment, so she uses the formula P = , where P = monthly payment, C = amount of loan, r = interest rate ÷ 1200, and N = total number of monthly payments.

1. Why do you think that the interest rate, 7.25%, is divided by 1200 in the formula?
2. List the values for each variable to use in the expression on the right side of the formula. Be sure you find the total number of monthly payments, not just the number of years of payments.
3. Find the monthly payment for the roller coaster.