Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 6 - Section 6.1 - Angle Measure - 6.1 Exercises - Page 481: 91

Answer

$\approx$ 2.09 m/s

Work Step by Step

Suppose a point moves along a circle of radius $r$ and the ray from the center of the circle to the point traverses $\theta$ radians in time $t$. Let $ s=r\theta$ be the distance the point travels in time $t$. The angular speed of the point is $\omega=\theta/t$. The linear speed of the point is $v=s/t$. $ v=r\omega$. 1 revolution = $ 2\pi$ radians. ---------- The speed of the current equals the linear speed of a point on the tip of a paddle. $\theta$= $($100 rev$)\displaystyle \cdot\frac{2\pi\ rad}{1\ rev}=200\pi$ rad t= 1 min = 60 s $ v=\displaystyle \frac{s}{t}=\frac{r\theta}{t}=\frac{0.2\cdot 200\pi}{60}\approx$2.09439510239 $\approx$ 2.09 m/s
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