Unit 4 WebQuest - Internet Project
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 designed 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.
Guidance
Here are some additional questions and ideas you may want to consider for your project.
- How does changing the height or the length of a hill of a roller coaster affect the speed?
- 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.
- What physics principles are used in the design of roller coasters and other thrill rides? To find out, interview a physics teacher.
- 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?
- 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 10–1
Maurice is preparing his calculations to show the speed of his new roller coaster at the top of one of the hills. He wants to make his coaster comparable to Superman the Escape in speed. So, his coaster reaches its maximum speed of 100 miles per hour at the bottom of the second hill, which is 250 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.
- What will be the value of 2gh2? Why?
- 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?
- List the values for each variable to use in the expression on the right side of the formula.
- What is the speed of the coaster at the top of the second hill?
- Suppose you increase h1 until the value for 2gh1 is greater than the value of (v2)2 + 2gh2. What happens to the value of v1?
Lesson 11–2
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 5.75%. She wants to know the monthly payment, so she uses the formula 
where P = monthly payment, C = amount of loan, r = interest rate ÷ 1200, and N = total number of monthly payments.
- Why do you think that the interest rate, 5.75%, is divided by 1200 in the formula?
- 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.
- Find the monthly payment for the roller coaster.
Lesson 12–3
Drew is planning a trip to an amusement park. He is going with his friends Mark, Frank, Isabel and Alex. They are all excited to go on the new coaster; the coaster contains three cars that can each hold one person. They all want to ride with all the different groups of people at least once.(Example: Drew with Mark and Isabel, Drew with Mark and Frank and so on.) We will have to use statistics to determine the number of times they will have to ride the coaster for this to happen.
- Make a tree diagram of the different combinations for each ride. How many possible outcomes are there?
- Use the formula
to check your answer from Question 1.
- What do the answers from Questions 1 and 2 mean about our order of riding the roller coaster?
- How many times will they have to ride the roller coaster if the order they sit in doesn’t matter?
TEACHER NOTES
In this project, students will Design a roller coaster, determine the speed of the coaster at two locations, and show two options for financing the roller coaster. They will need to find formulas on the Internet for finding the speed of roller coasters and for calculating payments on various loans. Some formulas are given in the exercises, but you may want to have students research others. By completing this project, students should gain a better understanding of formulas and the topics in Unit 4. You may want to have students work in pairs on this project so they can collaborate to design a roller coaster, apply formulas, and propose payment options for financing the coaster.
The Guidance section of the Cross Curricular Project contains questions that would be good for a whole-class discussion and for providing interdisciplinary connections. You may want to collaborate with a science teacher at your school for the physics principles used in the design of a roller coaster. If you prefer, have each student research one of the questions in the Guidance section and add the information they find to the final presentation of their Cross Curricular Project.
Several Web sites are included in the project to help students in completing this Cross Curricular Project. Encourage students to find additional sites and to share those sites with other students.
Students will work on this project in Unit 4.
Lesson |
10–1 |
11–2 |
12–3 |
Page |
531 |
584 |
660 |
ANSWERS
Lesson 10–1
- It will be 0, since the height at the bottom of the hill is 0.
- v2 = 146.7 ft/s; g = 32 ft/s2; h1 = 250 ft; h2 = 0
- v1 =
or about 74.3 ft/s
- The value under the radical becomes negative and you cannot find the speed at the top of the hill. So, the coaster must be going too slow when it arrives at the hill.
Lesson 11–2
- Since the payments are monthly, you divide by 12 to get the monthly interest rate. You must convert 5.75% to a decimal to do the calculation, so that means to divide by 100. Then 12(100) = 1200, the number by which you divide.
- C = 100,000; N = 12(30) or 360; r = 5.75 ÷ 1200 or about 0.00479
The monthly payment is $5251.01.
Lesson 12–3
- Sample answer: These mean that the order we sit in the seats in the roller coaster matters when we ride.
If order does not matter they will only have to ride 10 times to have all possible combinations of people ride together.