Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 3 - Radian Measure and the Unit Circle - Section 3.4 Linear and Angular Speed - 3.4 Exercises - Page 131: 43


$16.6$ miles per hour

Work Step by Step

The formula to be used for solving this question is the formula for linear speed $v=r\omega$ where $r$ is the radius and $\omega$ is the angular speed. The formula for angular speed $\omega$ is $\omega=\frac{\theta}{t}$. Since the tires rotate 215 times each minute, $\omega=\frac{\theta}{t}=\frac{\pi\times215}{1}=430\pi$ radians per min Substituting the values of $r$ and $\omega$ in the formula for linear speed: $v=rw=13(430\pi)=5590\pi\approx17561.5$ inches per min Since 1 foot equals 12 inches, $17561.5$ inches per min equals $\frac{17561.5}{12}=1463.5$ ft per min Since 1 mile equals 5280 feet, $1463.5$ ft per min equals $\frac{1463.5}{5280}=0.2772$ miles per min Miles per min can be converted to miles per hour by multiplying by 60: $0.2772\times60=16.6$ miles per hour
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