(The e-tool is not required)

Instructions:

17-C1

a. Identify the escape heights on the model for at least 16 different possible seat positions. The seat could be in the pit, high in the air, or right at ground level. Remember that this position depends on the angle of the rides rotation when it broke down. The radius of the graph wheel will be referred to as one unit. That is, a model height of one unit corresponds to an actual height of 100 feet on the ride, so an actual height of 80 feet on the ride will be represented by a measured height of 0.8 units on the graph.

b. Record your data a table

c. Suppose you were asked to add 20 more data points to your table. What shortcuts could you use to reduce the amount of work? Write a Summary Statement of your answer. Your answer is your summary statement (1 point for the correct answer and 1 point for your answer written in a complete sentence) and you will need at least 3 pieces of supporting evidence (1 point for each piece of supporting evidence)

17-2

a. Write an equation and use it to calculate the height of the triangle. Does the calculated escape height seem reasonable when compared to the data you collected in problem 17C-1? Write a summary statement (1 point for the correct answer and 1 point for your answer written in a complete sentence) with three pieces of supporting evidence (1 point for each piece of supporting evidence).

b. Write an equation representing the escape height () for any passenger (1 point for the correct equation), that is, for any angle of rotation of The Screamer. Note that the symbol is the angle represented by the Greek letter theta.

c. Using your table and graph from 17C-1b, add the graph of your equation from 17C-2b. How well does () fit your data from 17C-1b? Write a summary statement (1 point for the correct answer and 1 point for your answer written in a complete sentence) with two pieces of supporting evidence (1 point for each piece of supporting evidence).

d. Zoom out so that you can see more of the graph of (). Describe the behavior of the graph as gets larger. Does this make sense? Why or why not? Write a summary statement (1 point for the correct answer and 1 point for your answer written in a complete sentence) with three pieces of supporting evidence (1 point for each piece of supporting evidence).

# 17C-1 Problem Description "HURRY!!! Let's get there before the line gets too long!" shouts Antonio to his best friend Renn as they race to get on The Screamer, the newest attraction at the local amusement park. "It's only been open for one day, and already everyone is saying it's the scariest ride at the park!" exclaims Antonio. "I hear they really had to rush to get it done in time for summer." WELCOME TO THE Antonio whistles as he screeches to a halt in front of the huge sign that says, "Welcome to The Screamer, the Scariest Ride on Earth." The picture below it shows an enormous wheel that represents The Screamer, with its radius of 100 feet. Half of the wheel is below ground level, in a very dark, murky pit with water at the bottom. As The Screamer rotates at dizzying speeds, riders fly up into The the air before plunching downward through blasts of freezing air, hair raising screams, and sticky spider webs into the pit where they splash through the dark, eerie water on their way back above ground. SCREAMER ! SCARIEST RIDE UUS EARTH Renn and Antonio wait impatiently to get on the ride, watching passengers load and unload. New passengers get on and strap themselves in as others emerge from the pit looking queasy. The ride rotates 15 to load and unload the next set of riders. As Renn straps himself in, he remembers Antonio's ominous words, "I hear they really had to rush to get it done in time for summer." Sure enough, just as the ride plunges Renn and Antonio into the greasy water, they hear the piercing screech of metal twisting. Sparks fly and the pit fills with smoke as the ride grinds to a halt. To escape, all of the passengers must climb vertically to ground level from wherever they got stuck, either up from the pit or down from dizzying heights. Your Task: Write a function that describes how far above or below the platform a ride is when The Screamer breaks down. 17C-1a To help you gather data, you will use two Desmos eTools. Using this eTool, to identify the escape heights on the model for at least 16 different possible seat positions. The seat could be in the pit, high in the air, or right at ground level. Remember that this position depends on the angle of the ride's rotation when it broke down. The radius of the graph wheel will be referred to as one unit. That is, a model height of one unit corresponds to an actual height of 100 feet on the ride, so an actual height of 80 feet on the ride will be represented by a measured height of 0.8 units on the graph. Record your data in the table of this eTool. 17C-1b (5 points) 17C-1c (5 points) Suppose you were asked to add 20 more data points to your table. What shortcuts could you use to reduce the amount of work? Write a Summary Statement of your answer. Your answer is your summary statement (1 point for the correct answer and 1 point for your answer written in a complete sentence) and you will need at least 3 pieces of supporting evidence (1 point for each piece of supporting evidence). 17C-2 The function that models the situation in problem 17C-1 is a new parent function. To help you figure out what it is, use the triangle at right. 40 17C-2a With your team, write an equation and use it to calculate the height of the (5 triangle. Does the calculated escape height seem reasonable when compared to points) the data you collected in problem 170-1? Write a summary statement (1 point for the correct answer and 1 point for your answer written in a complete sentence) with three pieces of supporting evidence (1 point for each piece of supporting evidence). 17C-2b Write an equation representing the escape height h() for any passenger (1 point (1 point) for the correct equat that for any angle of rotation of The Screamer. Note that the symbol is the angle represented by the Greek letter "theta." 17C-2c Using your table and graph from 17C-1b, add the graph of your equation from (4 17C-2b. How well does h(0) fit your data from 17C-1b? Write a summary points) statement (1 point for the correct answer and 1 point for your answer written in a complete sentence) with two pieces of supporting evidence (1 point for each piece of supporting evidence). 17C-2d (5 points) Zoom out so that you can see more of the graph of h(e). Describe the behavior of the graph as 8 gets larger. Does this make sense? Why or why not? Write a summary statement (1 point for the correct answer and 1 point for your answer written in a complete sentence) with three pieces of supporting evidence (1 point for each piece of supporting evidence). # 17C-1 Problem Description "HURRY!!! Let's get there before the line gets too long!" shouts Antonio to his best friend Renn as they race to get on The Screamer, the newest attraction at the local amusement park. "It's only been open for one day, and already everyone is saying it's the scariest ride at the park!" exclaims Antonio. "I hear they really had to rush to get it done in time for summer." WELCOME TO THE Antonio whistles as he screeches to a halt in front of the huge sign that says, "Welcome to The Screamer, the Scariest Ride on Earth." The picture below it shows an enormous wheel that represents The Screamer, with its radius of 100 feet. Half of the wheel is below ground level, in a very dark, murky pit with water at the bottom. As The Screamer rotates at dizzying speeds, riders fly up into The the air before plunching downward through blasts of freezing air, hair raising screams, and sticky spider webs into the pit where they splash through the dark, eerie water on their way back above ground. SCREAMER ! SCARIEST RIDE UUS EARTH Renn and Antonio wait impatiently to get on the ride, watching passengers load and unload. New passengers get on and strap themselves in as others emerge from the pit looking queasy. The ride rotates 15 to load and unload the next set of riders. As Renn straps himself in, he remembers Antonio's ominous words, "I hear they really had to rush to get it done in time for summer." Sure enough, just as the ride plunges Renn and Antonio into the greasy water, they hear the piercing screech of metal twisting. Sparks fly and the pit fills with smoke as the ride grinds to a halt. To escape, all of the passengers must climb vertically to ground level from wherever they got stuck, either up from the pit or down from dizzying heights. Your Task: Write a function that describes how far above or below the platform a ride is when The Screamer breaks down. 17C-1a To help you gather data, you will use two Desmos eTools. Using this eTool, to identify the escape heights on the model for at least 16 different possible seat positions. The seat could be in the pit, high in the air, or right at ground level. Remember that this position depends on the angle of the ride's rotation when it broke down. The radius of the graph wheel will be referred to as one unit. That is, a model height of one unit corresponds to an actual height of 100 feet on the ride, so an actual height of 80 feet on the ride will be represented by a measured height of 0.8 units on the graph. Record your data in the table of this eTool. 17C-1b (5 points) 17C-1c (5 points) Suppose you were asked to add 20 more data points to your table. What shortcuts could you use to reduce the amount of work? Write a Summary Statement of your answer. Your answer is your summary statement (1 point for the correct answer and 1 point for your answer written in a complete sentence) and you will need at least 3 pieces of supporting evidence (1 point for each piece of supporting evidence). 17C-2 The function that models the situation in problem 17C-1 is a new parent function. To help you figure out what it is, use the triangle at right. 40 17C-2a With your team, write an equation and use it to calculate the height of the (5 triangle. Does the calculated escape height seem reasonable when compared to points) the data you collected in problem 170-1? Write a summary statement (1 point for the correct answer and 1 point for your answer written in a complete sentence) with three pieces of supporting evidence (1 point for each piece of supporting evidence). 17C-2b Write an equation representing the escape height h() for any passenger (1 point (1 point) for the correct equat that for any angle of rotation of The Screamer. Note that the symbol is the angle represented by the Greek letter "theta." 17C-2c Using your table and graph from 17C-1b, add the graph of your equation from (4 17C-2b. How well does h(0) fit your data from 17C-1b? Write a summary points) statement (1 point for the correct answer and 1 point for your answer written in a complete sentence) with two pieces of supporting evidence (1 point for each piece of supporting evidence). 17C-2d (5 points) Zoom out so that you can see more of the graph of h(e). Describe the behavior of the graph as 8 gets larger. Does this make sense? Why or why not? Write a summary statement (1 point for the correct answer and 1 point for your answer written in a complete sentence) with three pieces of supporting evidence (1 point for each piece of supporting evidence)