Nguyen N.

# Design Roller Coaster

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 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

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

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.

By:

Tutor
4.6 (42)

Tutor to Pique Your Sciences Interest

## Still looking for help? Get the right answer, fast.

Get a free answer to a quick problem.
Most questions answered within 4 hours.

#### OR

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.