Design Roller Coaster
Please Helpp! I need to design a roller coaster
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 roller coaster 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 roller coaster : Logarithmic, exponential, trigonometric, rational, polynomial
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
A good starting point is the Desmos calculator below
2. 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
3. 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.