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Ferris Wheel Trigonometric Modelling

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Ferris Wheel Trigonometric Modelling

Ferris wheel diagram

🎡 Part 1: Problem Setup and Mathematical Selection

Ferris Wheel Specifications:

• Diameter: 40 metres
• Centre height above ground: 25 metres
• Rotation time: 8 minutes (anticlockwise)
• Starting position: bottom of the wheel

1. What is the problem asking you to find?
2. List three reasonable assumptions you will make for this model:

a) ________________________________________________

b) ________________________________________________

c) ________________________________________________

3. Which type of function is most appropriate for modelling this situation?

Linear function

Quadratic function

Trigonometric function

Exponential function

4. Explain why this type of function is suitable:

📐 Part 2: Model Development and Calculations

5. Complete the function parameters:

For h(t) = A sin(Bt + C) + D, where h is height in metres and t is time in minutes:

• Amplitude A = _______ metres

• Period coefficient B = _______

• Phase shift C = _______

• Vertical shift D = _______ metres

6. Write the complete height function:

h(t) = ________________________________________________

7. Use your model to calculate the height at these times:

• At t = 0 minutes: h(0) = _______ metres

• At t = 2 minutes: h(2) = _______ metres

• At t = 4 minutes: h(4) = _______ metres

• At t = 6 minutes: h(6) = _______ metres

8. Sketch your function on the coordinate plane below:

🔍 Part 3: Interpretation and Communication

9. What are the maximum and minimum heights reached by the carriage?

Maximum height: _______ metres

Minimum height: _______ metres

10. At what times during the first complete rotation is the carriage at ground level (5 metres)?
11. Extension: A second carriage starts 4 minutes after the first. When will both carriages be at the same height for the first time?
12. Explain how this mathematical model could be applied to other real-world situations involving circular or periodic motion:

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