4. A cyclist is travelling in a straight path at a constant speed along a dirt road with a button stuck to the outside of one of their wheels. The movement of the button (as viewed from the side) can...

Extracted text: 4. A cyclist is travelling in a straight path at a constant speed along a dirt road with a button stuck to the outside of one of their wheels. The movement of the button (as viewed from the side) can be described using the equations of a cycloid, x = r(t – sin t), y = r(1 – cos t) where t represents the angle through which the wheel has rotated and r represents the radius of the wheel. See https://en.wikipedia.org/wiki/Cycloid or https://www.youtube.com/watch?v=x0Z9OeJbRy4 for more details! (a) Every time the button touches the ground, it leaves a mark on the dirt. If the marks are 647 cm apart, what is the radius of the tire wheel? (b) What value(s) of t correspond to the button touching the ground? 0. Does this mean that the cyclist is (c) Show that when t = 27, we have stopped? Why or why not? dt