# THE BJ DROP

### Best Roller Coaster By: Abhisek, Bikram, Herman and Kunal

## Summary for the Roller Coaster

## Problems and Solutions for the Roller Coaster

While making the roller coaster, we came across many problems, which included overlaps, smoothing, and fixing restrictions. When we zoomed in on the roller coaster at the start of each equation, we would see an overlapping, that would make the roller coaster have rough edges. When we first seen this, we tried fixing the restriction, but that was not the problem, so we decided to play around with the variables and found out that, that was the problem. We then went ahead to fix each equation, so we wouldn't see any overlaps. After we solved the overlapping issue, we noticed that the rough lines were also solved. Lastly, the last problem we came across was restricting the lines so that the roller coaster flowed properly, and by this we had to play around with the restricting numbers, but we needed to go in the third decimal place to get better results, and get proper connections between each equation.

## Descriptions and Equations

## Height v.s. Time

## Equation: Linear Function

- B value is 20, therefore a straight line

-This function is used to make the base of our roller coaster, where the riders will get on

## Equation: Sine Function

- A vertical stretch by a factor of 40 units

- A horizontal compression by a factor of 0.3 units

- A horizontal shift by 4.42 units to the right

- A vertical shift up 80 units

- This equation was used to make a drop and rise for our second drop

## Equation: Polynomial Fuction

- A vertical compression of 0.00005 units

- A vertical shift 94.5 units up

-This equation is used to connect our first drop all the way up to our second drop, also we used it as a fifth degree because we wanted a lot of ups and downs that were a lot less extreme

- We used a factor with a power of 3 to have the roller coaster approach the x-intercept and go back down again after touching it

## Equation: Logarithmic Function

- A vertical shift 40 units up

- A horizontal shit 82.831 units to the right

- A base close to 0, because it would rapidly curve the line towards infinity in the x

- This equation was to used to create a downwards slope for the roller coaster, and we used a number between 0 and 1 to do so

## Equation: Rational Function

- A vertical stretch of 100

- A horizontal shift to the right by 84.415 units

- A vertical shift 128.455 units up

- This equation creates a drop for our roller coaster, which is the last drop better it ends

## Equation: Quadratic Function

- A reflection about the x-axis

- A vertical stretch by a factor of 2.3

- A horizontal shift 28.5 units to the right

- A vertical translation of 300 units up

-This equation was used to make the arc of the roller coaster, where it would climb and then drop from

## Equation: Exponential Function

- A vertical stretch by a factor 1.27055

- A vertical translation 18 units up

- This equation was used to create our first rise for the roller coaster

- Exponential growth