Roller Coaster Initial Sheet

7/30/2019 Roller Coaster Initial Sheet

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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



Maximum Height at Peak 1: 193.46


FUN FACTOR:

Roller Coaster C





FUN FACTOR:

Roller Coaster D







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

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Roller Coaster Initial Sheet