4. (5 marks). 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} :r. = *r(t sint), y = r[1 cost) where t represents the angle through which the wheel has rotated and 1" represents the radius of the wheel. See https: {fen.wikipedia.orgfwiinycloid or https:ffww.youtube.com/watch?V=XUZQOerRy-l for more details! a Ever time the button touches the ound it leaves a mark on the dirt. If the 3' gr 1 marks are 47r cm apart, what is the radius of the tire wheel? (b) What value(s) of t correspond to the button touching the ground? (c) Show that when t = 211', we have E = U. Does this mean that the cyclist is a: stopped? Why or why not