Speed Coasters Inc: The Apocalypse

Description of The Apocalypse

The Apocalypse is an aggressive thrill which will leave riders with a great rush of adrenaline. With Apocalypse's high speeds, tall heights and rapid changes in both elevation and direction, makes it a thrilling attraction for all riders.

• Duration: 100 seconds
• Height: 300 ft.
• Speed: 148 km/h
• Manufacturer: Speed Coasters Inc.
• Model: Hypercoaster
• Location: Royal Gray Lion Amusement Park

Summary of our Plan:

To begin with, we created a sketch of a rough roller-coaster on a piece of paper, outlining the different functions that were required. The rollercoaster starts off with a linear equation to show the minimum point of 10ft where the passengers would get on. As the linear function progresses, it connects with an exponential function that starts leading our linear function into the pathway of a slight curve. Knowing the basic path that a roller coaster travels, we used a quadratic function or a parabola to create the basic rollercoaster drop. This parabola has a maximum height of 300ft in order to correctly meet the requirements. We used half of a sinusoidal function to join with the quadratic function since it would be able to create a drop and lead us into another peak on the rollercoaster. Various other functions, like the cubic, rational, and logarithmic were used to create parabolic paths that the roller coaster can travel. Our original roller coaster includes a loop, however, since we were required to create a height versus time graph, this loop was converted into a parabola on Desmos. The roller-coaster ends off with another horizontal line at the minimum height of 10ft to illustrate the end of the ride.

While creating the rollercoaster, we faced a few obstacles. The main difficulty that our group experienced was setting the appropriate domains for the different functions to connect correctly. The problem was that the two different functions that we wanted to connect were overlapping one another and therefore, this did not allow for a smooth pathway. However, we continued to try different values by creating equations with different stretches or translations which would connect the functions together.

Written Report:

The types of functions we utilized include:

Linear: straight line when plotted and in the form of y=mx+b

Domain for Equation 14: {XER; 94 ≤ x ≤ 100}

Quadratic: A degree two polynomial function in the form of y=a[k(x-d)^2 + c

Polynomial Functions: A polynomial function is a function such as a quadratic, a cubic, a quartic, and so on, involving only non-negative integer powers of x.

Simulation of The Apocalypse

Apocalypse Roller coaster

What do Critics think of the Apocalypse?

"A roller coaster which is composed of both exhilaration and adrenaline." - Coasters Review

Calculating the Instantaneous Rate of Change:

Therefore, the instantaneous rate of change at 35 seconds -8.24ft/second.