12 One of the rides at a theme park is a room where the floor and ceiling both move up and down for \(10 \pi\) seconds.
At time \(t\) seconds after the ride begins, the distance \(f\) metres of the floor above the ground is
$$f = 1 - \cos t$$
At time \(t\) seconds after the ride begins, the distance \(c\) metres of the ceiling above the ground is
$$c = 8 - 4 \sin t$$
The ride is shown in the diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{6a03a035-ff32-4734-864b-a076aa9cbec0-16_448_766_932_635}
12
- Show that the initial distance between the floor and ceiling is 8 metres.
[0pt]
[1 mark]
\includegraphics[max width=\textwidth, alt={}]{6a03a035-ff32-4734-864b-a076aa9cbec0-17_2500_1721_214_148}