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2 Your motion can be modelled using the formula h = a + b cos ct where h is the height of the car in metres, t is the time that has elapsed in minutes and a, b and care constants. Find values for a, b and c that will effectively model your motion on the big wheel.

2 Your motion can be modelled using the formula h = a + b cos ct where h is the height of the car in metres, t is the time that has elapsed in minutes and a, b and care constants. Find values for a, b and c that will effectively model your motion on the big wheel.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve part 2,3,and 4 

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
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
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 Prepare a Research Report for this investigation. Your final paper will be based on the following modified IB Mathematics Rubric:
Transcribed Image Text: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 Prepare a Research Report for this investigation. Your final paper will be based on the following modified IB Mathematics Rubric:
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