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Name:___________________________________ Date:_________________________ Band:________
Calculus | Packer Collegiate Institute
Roller Coaster: How Sweet It Is
Sweet!Dude!Sweet!Dude!Dude, Wheres My Car?
Weve talked about all the various things that make a roller coaster fun. But if you own an amusement park,
and you are deciding what roller coaster to build and you have a couple ideas, how do you know if one roller
coaster is more fun than another one?
Roller Coaster I1
Roller Coaster II2
Also, if you are the owner of an amusement park, you also need to take into account the costof the roller
coaster. You can build a super humungaloid crazy fun roller coaster, but if it costs too much, youre never
going to sell enough tickets to recoup the money you spent building it.
1http://www.ultimaterollercoaster.com/coasters/reviews/kentuckyrumbler/img/rumbler_2046_0.jpg
2https://reader009.{domain}/reader009/html5/0424/5adebd50543b8/5adebd52cd29e.jpg
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For our roller coaster project, you need to design a roller coaster which is super fun, but which also doesn t
cost an arm and a leg to build. For now, lets focus on how fun a roller coaster is. Mr. Kinnell and Mr. Shah
have come up with a formula which they think tells howfun a roller coaster is.
max slope max slopepeak 1 height peak 2 height length of track going do
total length of trackfrom peak 1 from peak 10,000
2...
500 500Fun
Instead of analyzing this, lets apply it to see whats going on. Heres a sample roller coaster with some data:
Amount of track going upwards: 2000 feet
Amount of track going downwards: 2100 feet
Total Amount of Track: 4100 feet
Now the fun factor is going to be:
1.430 2100
10,000 6607500 4 0
510
Fun
Lets look at each part of the fun factor equation
(1) The 10,000 is constant, so that just stays there.(2) If the peak were higher, would it make the fun factor lower or higher? Why?
As an amusement park patron, does a higher peak result in a more fun coaster? YES / NO
(3) If the decline were more gradual the whole way down, would it make the fun factor lower or higher? Why?
As an amusement park patron, does a gradual descent result in a more fun coaster? YES / NO
Height of peak 1 = 430 ft
Most negative slope = -1.5
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(4) If the roller coaster were changed so that 2100 feet of the track were going upwards, and only 2000 feet of thetrack were going downwards, would the fun factor be lower or higher? Why?
As an amusement park patron, is a roller coaster which goes down a lot more fun than a roller coaster which
goes up a lot? YES / NO
***
Now you hopefully understand some of the rationale behind the fun factor.
Take a total of2 minutes, and without any actual numbers, talk with your partner and see if you can predict the
order of thesefourroller coasters in terms of fun-ness, from the least fun to the most fun.
Roller Coaster A Roller Coaster B
Roller Coaster C Roller Coaster D
Remember, this is a quickestimate of fun-ness. Well actually calculate the fun factor below.
LEAST FUN MOST FUN
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Now well actually calculate the fun factor for each of them
Roller Coaster A
Amount of Track Going Downwards: 2394.31 feet
Amount of Track Total: 3142.06 feet
Maximum Height at Peak 1: 327.76 feet
Maximum Slope descending from Peak 1: -0.30
FUN FACTOR:
Roller Coaster B
Amount of Track Going Downwards: 1679.31 feet
Amount of Track Total: 3034.42 feet
Maximum Height at Peak 1: 193.46
Maximum Slope descending from Peak 1: -0.23
FUN FACTOR:
Roller Coaster C
Amount of Track Going Downwards: 1511.16 feet
Amount of Track Total: 3122.65 feet
Maximum Height at Peak 1: 396.45 feet
Maximum Slope descending from Peak 1: -0.40
FUN FACTOR:
Roller Coaster D
Amount of Track Going Downwards: 1629.43 feet
Amount of Track Total: 3077.69 feet
Maximum Height at Peak 1: 133.56 feet
Maximum Slope descending from Peak 1: -0.20
Maximum Height at Peak 2: 183.19 feet
Maximum Slope descending from Peak 2: -0.32
FUN FACTOR:
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Reflection:
(a) Now that youve completed this, explain why you think the coaster with the highest fun factor had such a
high fun factor. Why did it beat out the other three?
(b) How might you modify the two-peaked roller coaster so that it beat out the most fun roller coaster?
(c) As an amusement park owner, you have to estimate the cost of buying the metal for tracks as well as the
metal for the roller coaster support (the up-down braces are drawn on the roller coasters above) Just
eyeballing it, which one do you think uses the least metal, and which one do you think uses the most metal?
LEAST METAL MOST METAL