University : University of Tasmania UniLearnO is not sponsored or endorsed by this college or university.
Subject Code : XPD007
Assignment Task

 

 

Overview
The goal of this project is to design a rollercoaster to meet the specifications given.

 

Rollercoaster Criteria
A roller coaster is the graph of a function R(x) with domain [0,200] such that:
• the roller coaster starts on the ground: R(0) = 0.
• the graph of the rollercoaster must be a function. There are no loops.
• the length of the rollercoaster is 200m long 0 ≤ x ≤200
• the maximum height of the roller coaster is 75 meters: R(x) ≤ 75 for all x ∈ [0,200].
• the roller coaster does not go underground: R(x) ≥ 0 for all x ∈ [0,200].
• the ride is smooth: R(x) is continuous everywhere on its domain.
• the angle of steepest descent for the roller coaster is never more than 80 degrees (4π/9 radians).
• At least three equations of different types of functions must be used to define the rollercoaster:
o logarithmic, exponential, trigonometric, rational, polynomial

 

Submission
A report that outlines the design of your rollercoaster.
Your rollercoaster must be defined Algebraically and Graphically. All calculations should be neatly presented by hand or typed.
1. Graphical Component
• Meet the Criteria outlined above.
• Draw your graph in Desmos (or GeoGebra or similar graphing software).
• The starting point for your roller coaster should be the origin.

 

Algebraic Component

• The equation for the graph of the roller coaster is clearly listed as a piecewise function.
• Identify the sections of your function that are increasing and decreasing.
• Identify the Domain of your Function.
• Identify the Range of your Function.
• Identify the coordinates of local maxima and minima. These turning points may be
located graphically. Calculations to identify the turning points are not required.

 

Calculations
Calculations are required to show:
• The maximum height is 75m.
• The maximum angle in any section of descent is less than 80 degrees.
• The function is continuous. This involves substituting x values into the function, a sample calculation is shown below.

 

Verification Quiz
A 20min verification quiz with 10 questions based on the content of the assignment. The quiz will focus on explanation questions or ask for specific examples to allow you to demonstrate your understanding.

 

 

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  • Uploaded By : Brett
  • Posted on : March 13th, 2019
  • Downloads : 304

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