Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Transcribed Image Text:3 Create a cosine function for a big wheel with any diameter, rotational speed and central
axle height. Be sure to do the following:
Fully explain your formula (describe what and why). This may require graphs,
tables, etc.
Define and describe all variables as needed.
Describe the realistic scope and limitations of the variables (h, t) and parameters
(a, b, c)- in other words, describe real-world limitations on your model variables
and parameters and how these would affect your model - what would the real-life
model look like?
Be clear, concise and complete.
4 Optional extension question
Huw is on the original big wheel from Question 1. He becomes scared and starts
screaming when he is 50 metres or more above the ground.
When will Huw first start screaming?
a
b How long will he scream for?
5 Write up
following modified IB Mathematics Rubric:
Prepare a Research Report for this investigation. Your final paper will be based on the
Adapted criteria
coherence of the task.
Criterion A: Presentation: The presentation' criterion assesses the organization and
Achievement level
0
1
2
3
Descriptor
No attempt has been made to structure the project.
The task has some coherence or some organization.
The task has some coherence and shows some organization.
The task is coherent and well organized.
assesses use of appropriate mathematical language, key terms, multiple
Criterion B: Mathematical Communication: The mathematical communication' criterion
and deductive method.
wheel
Transcribed Image Text:Activity: Big wheel
(Student version)
A big wheel (like, for example, the
Singapore Flyer) has a diameter of 40 metres
and rotates around an axle that is 30 metres
above the ground. It takes 3 minutes to
complete one full rotation.
You decide to ride the big wheel and get into
one of the cars when it is at its lowest point.
Questions
1 Using the axes below, sketch a graph to show how your height varies over time.
Height in metres
90
DLE
80
70
60
50
40
30
20
10
2
Kittiphan/stock.adobe.com
3
DYNAMIC
LEARNING
2 Your motion can be modelled using the formula
h = a + b cos ct
4
5
Time in minutes
6
7
8
where h is the height of the car in metres, t is the time that has elapsed in minutes and a,
b and c are constants.
Find values for a, b and c that will effectively model your motion on the big wheel.
Mathematics for the IB Diploma: Applications and interpretation
Huw Jones 2019
9
Big wheel
1
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