Question 8
A ride at an amusement park consists of a small circle which rotates inside a large circle. The large circle, of radius $100$ metres, is tangent to the ground at its lowest point, and remains fixed in place throughout the ride. The smaller circle has radius $20$ metres. It is initially tangent to the larger circle at its lowest point. Ada sits in the ride at this tangent point, on a seat attached to the smaller circle. When the ride starts, the smaller circle rolls around the larger circle without slipping, so that the circles always remain tangent, and Ada rotates with the smaller circle, as illustrated below.
When the centre of the smaller circle has rotated $120^\circ$ around the centre of the larger circle, how far in metres is Ada off the ground?
When the centre of the smaller circle has rotated $120^\circ$ around the centre of the larger circle, how far in metres is Ada off the ground?