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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– cost) 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 64T 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 = 27, we have d = 0. Does this mean that the cyclist is stopped? Why or why not?

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– cost) 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 64T 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 = 27, we have d = 0. Does this mean that the cyclist is stopped? Why or why not?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.3: Hyperbolas
Problem 35E
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4. A. 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 – cost) %3D 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 64T 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 2T, we have = 0. Does this mean that the cyclist is stopped? Why or why not? %3D dt
Transcribed Image Text:4. A. 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 – cost) %3D 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 64T 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 2T, we have = 0. Does this mean that the cyclist is stopped? Why or why not? %3D dt
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