Figure 4 shows a sketch of a Ferris wheel - Edexcel - A-Level Maths Pure - Question 12 - 2022 - Paper 2

To establish the full model for the height of a passenger on the Ferris wheel,

1. Determine A:

   • The maximum height is given as 50m. Thus, we set:

   $A = 50$

2. Determine b:

   • Since the wheel takes 720 seconds for one complete revolution, the angular frequency, b, must be calculated as follows:

   $b = \frac{2\pi}{720} \approx 0.00872665 \approx 0.00873\; (3\; significant\; figures)$

3. Determine α:

   • The passenger is 1m above the ground at the start, i.e., when t = 0, we have:

   $H(0) = |A\sin(0 + α)| = 1$

   Knowing that A = 50, this leads to:

   $|50 \sin(α)| = 1$

   Thus, solving:

   $\sin(α) = \frac{1}{50} = 0.02$

   • Calculating α gives:

   $α = \arcsin(0.02) \approx 0.02003 \approx 0.020\; (3\; significant\; figures)$

Hence, substituting into the original model, we arrive at the complete equation:

$H = |50\sin(0.00873t + 0.020)|$.