Flight of Fear

Grand Dynamic Coasters Inc.

Grand Dynamic Coasters Inc.

Grand Dynamic Coasters Inc. was founded by Daniela Tab-One. After riding her first roller coaster at the age of 10, she knew she wanted to design roller coasters for living. After graduating MIT with honors in engineering she decide create her own company. Tab-One has designed and constructed more than 10 roller coasters, some of which are top attractions at amusements parks. Now, a new coaster in going to be added to your favorites list brought to you by Daniela Tab-One along with her well equipped staff. They are ready to unveil Flight of Fear. The newest roller coaster in a class well above normal coasters.

Flight of Fear

Roller Coasters are meant to make people scream, feel their insides being moved all around as they are shoved side to side, up and down. This new coaster is something you have not experienced before. It took a total of three months in planning to get everything down and right. This coaster is to be the greatest coaster ever made. Having numerous drops and head spinning turns, it will surely cause the normal rider true fear.

Quick Facts

Location: Empire Amusement Park

Duration: 100 seconds
Height Requirements: 55"
Maximum Height: 300 feet
Distance Off Ground: 10 feet
Manufacturer: Grand Dynamic Coasters Inc.
Maximum Speed: 150 km/h

Fun Facts

>First ride to go 150 km/h

>Empire Amusement Parks 20th Roller Coaster

>First Roller Coaster to touch 300 feet

Birth of Flight of Fear

Before any construction could be done, careful and well planned graphs were needed to be made. Multiple rough drafts were edited before one idea stuck with us. Then, that stretch was refined again until it was perfect. The idea here was to take a simple height vs time graph and apply mathematical functions to it.
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Final Copy

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  • During the creation of this rollercoaster we had discussed what we enjoyed the most on our favorite rollercoaster and put that into creating this. Things like multiple drops were taken into consideration and changing direction a lot. We found that having few bigger drops were not as fun as having smaller drops. Also we found that having a lot of changing directions (up and downs) made for a fun ride. At first we thought it would be easy to create a simple rollercoaster from a few equations learned this year but then having to get the numbers down correct and restrictions as well as making it look realistic proved to be a difficult task. We made simple graphs without transformations then slowly added transformations. When that was done we zoomed in on each and make sure they link correctly. Few equations needed to be deleted and switched for others because it made the rollercoaster transition smoothly. We also increased our time to 1000 making every 10 units one second. This gave us fewer decimals.

General Description of each equation

The Flight or Fear is a coaster like none other. This made from futuristic technology and designing will have the bravest of hearts quickly afraid of what awaits them.

The main goal for Grand Dynamic Coasters Inc. was to design and height vs time roller coaster with a few restrictions. The roller coaster had to be made with functions used in MHF4U0. Also it needed to complete itself in 100 seconds as well as keep between a height restriction of [yeR/10<y<300].

This coaster consists of multiple functions. A function can be described as a relation in where every x value has a different y value.

Since this was a height vs time graph, the x axis became time (independent variable), and the y axis became height (dependent variable).

1. y = 10

D{xeR|0 ≤ x ≤ 60.6} , D{xeR}


Horizantal line at y=10.

Horizantal line at y=10 with line starting at an x value of 0 and ending at x=60.6.

End behavior = x --> ∞, y = 10. X --> -∞, y = 10

Base Function=x

2. y=1.5(x-35)/15+8

D{xeR|59.7 ≤ x ≤ 190.8} , D{xeR}
R{yeR|y > 8}

A= Vertical stretch by factor of 1.5

K= Horizontal stretch 15

D= Shift 35 units right

C= Shift 8 units up

Base Function=1.5x

3. y=-[(x/5.1)-52.4]^2+300

D{xeR|190.8 ≤ x ≤ 263.455} , D{xeR}


A= Vertical reflection

K= Horizontal stretch by factor of 5.1

D= Shift 267.24 units right

C= Shift 300 units up

Base Function=x2

End behavior = x --> ∞, y --> -∞. X --> -∞ y --> -∞

4. Y=300cos[1/35(x-260)]+0.91

D{xeR|263.455 ≤ x≤ 283.089} , D{xeR}

R{yeR|-1 ≤ y ≤ 1} , R{yeR|-299.09 ≤ y ≤ 300.91}

A= Vertical stretch by factor of 300

K= Horizontal stretch by factor of 1/35

D= Shift 260 units right

C= Shift 0.91 units up

Base Function=cos(x)

5. Y=-[1/940(x-321)^3]+180

D{xeR} , D{xeR|283.089≤ x ≤ 325.0139}


A= Vertical reflection

K= Horizontal stretch by factor of 940

D= shift 321 units right

C= shift 180 units up

End behavior = x --> ∞, y --> -∞. X --> -∞ y --> ∞

6. Y=[1/99999(x-375)^4]+117

D{xeR|325.0139 ≤ x ≤ 334.5} , D{xeR}

R{yeR|y ≥ 117}

K= Horizontal stretch by factor of 99999

D= Shift 375 units right

C= Shift 1117 units up

Base Function=x3

End behavior = x --> ∞, y --> ∞ ; x --> -∞ y --> ∞

7. y=((x-364)/4)^2+90

Domain without restriction= [xeR]

Range without restriction= [yeR/90≤y]

Domain with restriction= [xeR/ 334.5≤x≤375.977]

Range with restriction=[yeR/ 90≤x≤144.391]

A= no transformation

K=horizontally stretch by a factor of 4

D= translated 364 units to the right

C=vertical translation up 90 units

Base Function= x^2

End Behaviors=x-->-∞, y-->∞

8. y=-csc((x-338)/5)+100

Domain without restriction= [xeR]

Range without restriction=yeR

Domain with restriction=[xeR/ 375.977≤x≤381.911]

Range with restriction=[yeR/98.336≤y≤99]

A=reflection in the x-axis

K=horizontally stretched by a factor of 5

D=translated 338 to the right

C=vertical translation 100 units up

Base Function= csc(x)

9. y=(2/((1/200(x-354) ) ))+80

Domain without restriction= [xeR/ x≠354]

Range without restriction=[yeR/ y≠84]

Domain with restriction=381.911≤x≤445.5

Range with restriction=88.372≤y≤98.3292

Vertical Asymptote= x=354

Horizontal Asymptote= y=84

A= vertical stretch by a factor of two

K= stretched by a factor of 200

D=translated 353 units to the right

C= translated 80 units up

Base Function= 1/x


Domain without restrictions= xeR

Range without restrictions= yeR/ 88.28≤y

Domain with restrictions= 445.5≤x≤461.84

Range with restrictions=88.36≤y≤109.15

A=no transformation

K=vertical stretch by a factor of 10.2

C=horizontal translation 440 units to the right

D=vertical translation 88.28 units up

Base Function=x^4

End Behaviors= x-->- ∞, y-->∞

11. y=100 log(x-452)+10

Domain without restrictions=452≤x

Range without restrictions=yeR

Domain with restrictions=[xeR/ 461.81≤x≤489.62]

Range with restrictions=yeR/ 110≤y≤167.5

A= Vertical stretch by a factor of 100

K=no transformation

D=translated 452 units to the right

C=translated 10 units up

Base Function=log(x)

12. y=-((x-525)^8/1000000000000)+170

Domain without restrictions=[xeR]

Range without restrictions=[yeR\y≤170]

Domain with restrictions=[xeR\489.625≤x≤566.3]

Range with restrictions=[yeR\161.5≤y≤170]

A=reflection in the x axis

K=Horizontal stretch by a factor of 1000000000000

D=translated 525 units to the right

C=translated 170 units up

Base Function=x^8

End Behaviors= x-->- ∞, y-->-∞

13. y=1.5(-x + 690 / 10) +10.9

D{xeR|566.32 ≤ x ≤ 703.47}

R{yeR|11.5≤ y≤ 161 }

A= Vertical stretch by factor of 1.5

K= Horizontal stretch 15

D= Shift 690 units right

C= Shift 10.9 units up

Reflected over x axis

Base Function= 1.5x

14. y=1.5(1/15(x-695))+10

D{xeR|703.47≤ x ≤ 760.373}

A= Vertical stretch by factor of 1.5

K= Horizontal stretch 15

D= Shift 695 units right

C= Shift 10 units up

Base Function=1.5x

15. y=-(1/20(x-778)^)3+30

D{xeR|760.537 ≤ x ≤ 830.2}


A= Vertical reflection Stretch of a factor of 1/20

D= Shift 77 units right

C= Shift 30 units up

Base Function=x

End behaviors of base function:
x--> ∞, y-->∞

16. Y=-log(x-668)+10

D{xeR|830.21≤ x≤ 1000}

R{yeR|12.2 ≤ y ≤12.5 }

A= Vertical reflection

C=Shift 10 units up

D= Shift 668 units right

Base Function=log(x)

Solve for at 12 feet

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Solve for at 250 feet

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Calculate average rate of change for 10-15 seconds and 50-60 seconds

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Solve for instantaneous rate of change

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