# Funzo the Parabola Theme Park

### Harman i Harshan i Rahul i Dennis

Indie/Pop/Folk Compilation - Summer 2015 (1-Hour Playlist)

## Vel' Stratos

The vel’ stratos was made for the purpose of moving fast with many jaw dropping drops. We thought through the possible ways we could set up where anything would happen. We wanted to have the ride work for as much speed as possible while maintaining a factor of suspense during each drop. From our personal experiences in roller coasters knew that the moment you get on the ride if would have to start off with a nice drop. That in mind, we thought by disturbing the drops at certain points would be beneficial for a better experience. After that we tried to smaller versions of the drop and had it end with a nice loop before the final drop. Some difficulty we had was just trying to get the right idea of what the group wanted to add and where we could place anything.

## Written Report

In the beginning of the roller coaster starts off with a linear function acting as a launch platform. Being parallel to the ground it does not climb and only serves to board and unboard the passengers. After the linear function [y=10], the roller coaster climbs from 5 to 14 seconds. This function is rational [-100/(x-15)] with a negative a value. After the climb the roller coaster approaches a sudden halt and then climbs for a short duration again from 14 to 18 seconds modeled by a degree 5 polynomial which has a root ≈11.959. After this final climb the roller coaster slowly approaches a dive. This final climb is modeled by a logarithmic with a horizontal stretch by a factor of 5 function from 18 to 24 seconds. As the roller coaster reaches the end of the third part it approaches a high speed dive. The dive is formed by a cubic function with a real root of 37.3681.The roller coaster having a large magnitude of kinetic energy then approaches another climb which runs from 35 to 60 seconds modeled by a quadratic function which forms a parabola opening downward. At the seventh part the second climb is completed and the roller coaster takes another dive and this part is modeled by a polynomial function with degree two and a root of 65 forming a parabola opening downward. As the roller coaster gains momentum again the roller coaster then approaches a series of crests and troughs with amplitude of 10 modeled by a cos function. After the sinusoidal function the roller coaster then proceeds to approach a dive of 190 m represented by an exponential function. After the final drop the roller coaster then slows down as it approaches the beginning of the linear track again.

## Calculations

The roller coaster reaches the height of 250 ft after:

• 14.6 seconds

• 25.36 seconds

• 59.83 seconds

• 70.32 seconds

This is determined by changing the y-value equal to 250.

It also reaches the height of 12 ft after:

• 6.67 seconds

• 99.13 seconds

This determined by changing the y-value to 12.

## Finding IROCs and AROC

The AROC where X1 = 10 and X2 = 15 equals 47.8

This is determined by Y2-Y1/X2-X1.

The AROC where X1=50 and X2= 60 equals 20.

Which is also determined by Y2-Y1/X2-X1.

## Instantaneous Velocity at 35 Seconds

By creating a line that intersects roughly and finding the slope of it we found the IROC

Point 1 = (35,137.5)

Point 2 = (37, 77.5)

77.5 - 137.5

37-35

= -30 ft per second

## Sections of the Ride

The rollercoaster is modelled by 10 functions. Consisting of linear, quadratic, polynomial of degree 3 and above, rational, sinusoidal, exponential and logarithmic functions.

There were many ways to find the domains of the functions, the main two ways are to simply use the graphing software and find where the two lines intersect or you can put the equations equal to each other and solve for X giving the domains, POI, of each line

## Linear

• Y- intercept = (0,10)

• Parallel to X-axis

• Range {y=10}
• Domain {xER II 0<X<5}

## Rational Function

• Non Uniform Rate of change

• Y- intercept = (none

• Domain {XER II 5<X<14.6}
• Range {YER II 10<y<255}

## Degree 5 function

• Non Uniform Rate of change

• Y- intercept = none

• Domain (XER॥ 14.6 <x< 18)

• Range (YER॥ 255 < y< 292)

## Logarithmic function

• Non Uniform Rate of change

• Y- intercept = (none

• Domain (XER॥ 18 <x< 24.2)

• Range (YER॥ 292 < y< 296.5)

## Cubic function

• Non Uniform Rate of change

• Y- intercept = none

• Domain (xER॥ 24.2 <x< 35.3)

• Range (yER॥ 296.5 >y> 125.6)

## Quadratic function

• Non Uniform Rate of change

• Y- intercept = none

• Domain (XER॥ 35.3 <X< 60.8)

• Range (yER॥ 125.6 < Y< 279.6)

## Degree four function

• Non Uniform Rate of change

• Y- intercept = none

• Domain (XER॥ 60.8 <x< 71.4)

• Range (YER॥ 279.6 < y< 195.1)

## Sinusoidal function

• Non Uniform Rate of change

• Y- intercept = (none

• Domain (XER॥ 71.4 <X< 90)

• Range (YER॥ 195.1 >Y> 209)

## Exponential function

• Non Uniform Rate of change

• Y- intercept = (none

• Domain (XER॥ 90 <X< 99)

• Range (YER॥ 19.1 <Y< 209)

## Logarithmic function

• Non Uniform Rate of change

• Y- intercept = (none

• Domain (XER॥ 99 <X< 100)

• Range (YER॥ 10 < Y< 19.1)