A Ferris wheel with diameter 72 metres rotates at a constant speed. The lowest point on the wheel is 8 metres above the ground, as shown on the following diagram. A seat starts at the lowest point.
The wheel completes one revolution in 12 minutes.
After t minutes, the height, h metres, of the seat above the ground is given by h(t)=acos(bt)+44, where a,b∈R.
(a) Find the value of
(a.i) a;
(a.ii) b.
(b) Sketch the graph of h, for 0≤t≤12. Clearly label the coordinates of the maximum point and the end points.
Consider one revolution of the Ferris wheel.
(c) The seat is at least 26 m above the ground for T minutes. Find the value of T.
(d.i) Find h′(t).
(d.ii) Hence or otherwise, find the time at which the height of the seat above the ground is decreasing at its fastest rate.