Speed Coasters Inc: The Apocalypse
Creators: Purva, Janice, Rinu, Saumya, and Aashi
Description of The Apocalypse
- 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
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
What do Critics think of the Apocalypse?
Train
Track
Station
At the boarding area, the station features three colour-coded cabinets for loose belongings- one designated for each of the three trains. The operator's booth is also located on this platform.
Solving for the exact time(s) when your rollercoaster reaches a certain height:
Calculating the Average Rate of Change:
Calculating the Instantaneous Rate of Change:
Contact:
Email: speedcoastersinc@rollercoasters.com
Website: www.speedcoastersinc.com
Phone: 1-800-2345
Facebook: facebook.com/speedcoastersinc.facebook.com
Twitter: @speedcoastersinc