Amplitude, period and midline of a cosine model for the height of a seat on a turning wheel

At a fairground, a large wheel with a diameter of \(48\) metres turns at a constant rate, making \(5\) complete turns every hour. The bottom of the wheel is \(3\) metres higher than the ground. A seat \(Q\) is fixed to the rim, and when the wheel starts to turn, \(Q\) is at the top of the wheel, as shown in the diagram.

The height of \(Q\) above the ground \(t\) minutes after the wheel starts to turn is \(h\) metres, where \(h(t)=a\cos(bt)+c\) and \(a\), \(b\) and \(c\) are constants with \(b>0\).

Find \(a\), \(b\) and \(c\).[5]