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. a) Every time the button touches the ground, it leaves a mark on the dirt. If the marks are 64π 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 = 2π, we have dx/dt = 0. Does this mean that the cyclist is stopped? Why or why not?

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. a) Every time the button touches the ground, it leaves a mark on the dirt. If the marks are 64π 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 = 2π, we have dx/dt = 0. Does this mean that the cyclist is stopped? Why or why not?

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter3: Motion In Two Dimensions

Section: Chapter Questions

Problem 30P: A point on a rotating turntable 20.0 cm from the center accelerates from rest to a final speed of...

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