# Kage Bunshin No Rollercoaster

### By: Harnoor and Abhishek

## Rough Sketch Of Rollercoaster

## Creation Process of the Rollercoaster

## Written Report

In our graph, time is an independent variable and height is a dependent variable. Throughout the graph, time is always increasing; however, height is the variable that keeps fluctuating. The graph starts at (0, 10) with both time and height increasing at the same time, this continues until 20s, where time is still increasing but the height of the graph starts to decrease. At 31s the height of the graph starts to increase, until at 34s it drops and pulls up again at 41.5s and once again drops, until it rises back at 43s. Afterwards, the height increases exceptionally faster than time, between 43s and 45s.

The height of the graph is increasing but almost seems to be at constant, between 45s to 60s. At 67.5s, our graph reaches its maximum height of 300ft. After reaching the maximum point, the height falls drastically to 10ft, while time is still increasing, until it reaches 100s.

__Equations and their restrictions__

y = 2^x+9{0≤x≤6.06}

y = -(x-20) ^2+270{6.06≤x≤30}

y = -35sin(x-30) +170{30≤x≤43.2529963582}

y = -1/x-45+147.24{43.2529963582≤x≤45}{147.81≤y≤250}

y = log(x=44.990268) +264.148{44.6≤x≤59.9825}

y = 4.34x+5{59.9825≤x≤62.8593}

y = -(x-67.57)^2 +300{62.8593≤x≤69}

y = -(x-68) ^3 +299{68.789≤x≤72.938804}{184.735<y}

y = 90 ^(x-74) +10{72.8≤x≤100}{184.735>y}

## Calculations

## Rollercoaster Graph Design

X- Axis : Time (seconds)

Max Height : 300 feet

Min Height : 10 feet