# Our Rollercoaster

### Made by Alvin, Juven, Gurwinder and Mandeep

## INTRODUCING THE MIDNIGHT DREAM

## Report

## Summary

We originally intended to create a roller coaster consisting of all the functions required and a very tall and steep drop. This would ensure the satisfaction of all the passengers since most people visit amusement parks because of the thrill that is associated with the rides. Furthermore, we had to set restrictions and values for the functions such as the phase shift in order to make a complete roller coaster. The proper use of values also ensured that the roller coaster runs smoothly which is an important factor of a good ride. We effectively made use of restrictions on functions in order to create an effective transition between the functions. Some struggles we encountered while creating the roller coaster were that we didn’t know which “a” values to use in order to efficiently connect two functions together. In addition, we had issues with making a smooth transition between two equations. We tried creating a realistic roller coaster, which could potentially be used at Wonderland or at any other amusement park. Additionally, this was a challenge we faced while creating the roller coaster because we had to control the angles of the drop and the distances between them.

## Rough Graph

## Equations

## Solutions

## Exact times the Roller Coaster Reaches 250 Feet

The height is 250 at 10, 16, 22, 28, 34, 54.1, and 66.667 seconds

## Exact time the Roller Coaster Reaches 12 Feet

The height is 12 at 85.58 seconds

## Average Rate of Change from 10-15 Seconds and from 50-60 Seconds

AROC from 10-15 seconds is -1

AROC from 50-60 seconds is 5

## Instantaneous Rate of Change at 35 Seconds

IROC at 35 seconds is -10