IB Functions Problem 020
At an amusement park, a Ferris wheel with a diameter of \(111\) metres rotates at a constant speed.
The bottom of the wheel is \(k\) metres above the ground.
A seat starts at the bottom of the wheel.
The diagram is not to scale.
The wheel completes one rotation in 16 minutes.
After \(t\) minutes, the height of the seat above the ground is given by \(h(t) = 61.5 + a\,\cos\left(\frac{\pi}{2}t\right)\), for \(0 \leq t \leq 32\).
- After \(8\) minutes, the seat is \(117\) m above the ground. Find \(k\).
- Find the value of \(a\).
- Find when the seat is \(30\) m above the ground for the third time.