Periodic phenomena and modelling
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A Ferris wheel has radius \(25\) feet, with its lowest point \(5\) feet above the ground. The wheel takes \(40\) seconds to complete one full revolution. A passenger boards at the lowest point at time \(t = 0\).
(i) Find the midline of the passenger's height.
(ii) Find the amplitude.
(iii) Find \(B\) (the coefficient on \(t\)) using the period.
(iv) Write the height function \(h(t)\) in the form \(h(t) = A \cos(B t) + D\). (Decide on the sign of \(A\) based on the starting position.)
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