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Rimini’s Ferris wheel has 42~transparent capsules that reach an altitude
of 55~m from where you can see the Romagna coast, from Gabicce to
Cesenatico.

The ticket costs 9€ and the trip lasts 30~minutes, during which the wheel
completes 5~turns.

The motion of a capsule is described by the function

$$h(t) = 28 - 27 \cdot \cos\left(\dfrac{\pi}{3}t\right)$$

where $h$ is the altitude of the capsule in metres and $t$ is time in minutes,
with $t = 0$ when the trip starts.

\begin{enumerate}
    \item \nbPointsEnumi{2}Determine the time taken for a complete turn and explain the
    meaning of the coefficient $\dfrac{\pi}{3}$ in the equation of $h(t)$.
    
    \item \nbPointsEnumi{3}Check that the maximum altitude is 55~m and determine after how
many minutes is attained.
    
    \item \nbPointsEnumi{2}Determine the altitude of the capsule when the trip starts, hence
determine the radius of the wheel.
\end{enumerate}
