Create a roller coaster model that incorporates various

Reference no: EM133613715

GRASP

Goal: To create a roller coaster model that incorporates various mathematical concepts, such as writing equations for parabolas and analyzing function attributes.
Role: You are an engineer tasked with designing and constructing a roller coaster model, combining your knowledge of mathematics and physics.
Audience: Your audience includes your mathematics teacher, classmates, and potentially anyone interested in roller coasters.
Situation: You have been asked to design a roller coaster model as part of your mathematics project. This project will showcase your ability to apply mathematical concepts to real-world scenarios and communicate your findings effectively.
Product: Your final product will consist of three parts:
Graph (Part A): You will create a graph of your roller coaster, with the x-axis representing time (t) in seconds and the y-axis representing height (h) in feet. The roller coaster should have a duration of at least 30 seconds (t ≥ 30) and should not exceed the height of the tallest roller coaster you've researched.

Equations (Part B): You will write equations for each section of the roller coaster graph, considering the Parabola (in your design). These equations will help explain the mathematical representation of the roller coaster's path.
Analysis (Part C)
In the roller coaster engineer project, you designed a graph to look like a roller coaster, as well as relate it to time and height. Now you are going to create a graph of a roller coaster only in relation to time and height.

PART A: At Ferrari world, complete the following tasks:
Video of a roller coaster:
Record a roller coaster ride while you are on it. Make sure the camera is facing forward. You do not necessarily need to be in the front seat, but it will be more helpful. Be careful to record the video from the moment it starts until it stops.
OR
Record a roller coaster ride while you are on the ground. Be careful to record the entire ride from the moment it starts until it stops. You will want the entire ride to fit in your video screen at all times.
Find a map/picture of the roller coaster, so you can see the complete path.
Find out the height at which the roller coaster begins and its highest point (approximately).

PART B: Create a Graph
Determine your domain and range before you create the scale on the graph. Again, let the x-
axis represent time (t) in seconds and the y-axis represent your height (h) in feet.
In order to create your graph, you will need to watch the video to determine the time you reach your minima and maxima. In addition, you will need to analyze the map/picture of the roller coaster to determine the approximate height of these turning points.
Remember, you are only relating your graph to time and height.
Therefore, if the roller coaster has a loop in it, you will not
draw a loop, rather a parabola that opens downward.

ROLLER COASTER ENGINEER

OBJECTIVE: You will create a roller coaster that demonstrates your knowledge and understanding of the following skills:
Write the equation for each section of the roller coaster (where you see a parabola)
Write a piecewise-defined function to represent the entire roller coaster.
Determine the height of the roller coaster at a specified time.
Identify function attributes:
Domain and Range
Local Minima and Maxima
Intervals of Increase and Decrease

PART A: Graph
Draw a graph of a roller coaster with the following guidelines:
Let the x-axis represent time (t) in seconds and the y-axis represent your height (h) in feet. Your
roller coaster needs to have a time of 30 seconds or higher (t ≥ 30). The height of your roller coaster should be or lower (h ≤ ) based on your research of the tallest roller coaster in the world.
You may need to use the following parent functions (optional):

Title your graph with the name of your roller coaster.

PART B: Write a Function

PART C: Analyze (Option1)
Answer the following questions:
What is the name of your roller coaster? How many seconds does it take to ride?

How many seconds does it take the roller coaster to reach its maximum height? What is the maximum height?

What is the domain and range of your roller coaster graph?

Identify an interval in which your roller coaster would be moving slow.

Identify an interval in which your roller coaster would be moving fast.

Using the intervals from numbers 4 and 5, determine which interval is increasing and which is decreasing.

Using function notation, what does f(12) = and what does this mean in relation to your roller coaster?

If 24 seconds has passed since the roller coaster started, what is the height of the roller coaster?

PART C: Analyze (Option 2) - Let's Go for a Ride!!!

Let's go for a ride on the roller coaster, which is seconds long. The roller coaster begins at meters above ground. After seconds we will reach the maximum height of feet. Therefore, the values for the domain of this roller coaster is and the range is . We will be moving slow during the intervals of , because we will be going (upwards/downwards), which means these are the intervals of. We will be moving very fast during the intervals, because we will be going (upwards/downwards. In function notation, f(12) = , which means at , the roller coaster ismeters high. After 24 seconds has passed, we will be at meters above ground.

Attachment:- U1 GraspTask.rar

Reference no: EM133613715

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