9.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{824d73c5-525c-4876-ad66-33c8f1664277-22_419_569_301_226}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{824d73c5-525c-4876-ad66-33c8f1664277-22_522_927_239_917}
\captionsetup{labelformat=empty}
\caption{Figure 5}
\end{figure}
Figure 4 shows a sketch of a Ferris wheel.
The height above the ground, \(H \mathrm {~m}\), of a passenger on the Ferris wheel, \(t\) seconds after the wheel starts turning, is modelled by the equation
$$H = \left| A \sin ( b t + \alpha ) ^ { \circ } \right|$$
where \(A\), \(b\) and \(\alpha\) are constants.
Figure 5 shows a sketch of the graph of \(H\) against \(t\), for one revolution of the wheel.
Given that
- the maximum height of the passenger above the ground is 50 m
- the passenger is 1 m above the ground when the wheel starts turning
- the wheel takes 720 seconds to complete one revolution
- find a complete equation for the model, giving the exact value of \(A\), the exact value of \(b\) and the value of \(\alpha\) to 3 significant figures.
- Explain why an equation of the form
$$H = \left| A \sin ( b t + \alpha ) ^ { \circ } \right| + d$$
where \(d\) is a positive constant, would be a more appropriate model.