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Figure 4 shows a sketch of a Ferris wheel - Edexcel - A-Level Maths Pure - Question 11 - 2022 - Paper 2
Question 11
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Figure 4 shows a sketch of a Ferris wheel. The height above the ground, H_m, of a passenger on the Ferris wheel, t seconds after the wheel starts turning, is modell... show full transcript
Worked Solution & Example Answer:Figure 4 shows a sketch of a Ferris wheel - Edexcel - A-Level Maths Pure - Question 11 - 2022 - Paper 2
Step 1
b) Explain why an equation of the form H = |A \, \sin(bt + \alpha)| + d would be a more appropriate model.
Answer
Using an equation of the form
Explanation
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Minimum Height Above Ground: The inclusion of the constant d allows the model to be shifted vertically, which means it can effectively account for the actual minimum height above the ground. In this case, d can represent the ground level, which was indicated as 1 m in the problem.
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Physical Interpretation: By adding d, you ensure that the model reflects the physical scenario where the height cannot drop below the ground level (0 m in a real-world scenario), enhancing the accuracy and realism of the model.
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General Fit: This form of the equation allows more flexibility in adjusting to different Ferris wheel configurations where the base height might not start from the ground itself, thus enabling a broader application.