Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 13: Vector-Valued Functions and Motion in Space - Practice Exercises - Page 776: 4



Work Step by Step

$v(t)=\dfrac{dr}{dt}=i[e^t(\cos t -\sin t) ]+j [e^t(\sin t +\cos t) ]$ and $a(t)=\dfrac{dv(t)}{dt}=-2 e^t ( \sin t i- \cos t j)$ Let us suppose that $\theta$ be the angle between $r$ and $a(t)$ Thus, $\theta =\cos^{-1} [\dfrac{r \cdot a(t)}{|r| |a(t)|}]$ or, $=arccos [\dfrac{ e^t \cos t \times (-2 e^t \sin t) +(e^t \sin t) (2e^t \cos t)}{\sqrt {(e^t \cos t )^2+(e^t \cos t )^2 \cdot \sqrt {(-2 e^t \sin t)^2 +( e^t \cos t)^2}}}]$ or, $\theta=\dfrac{\pi}{2}$
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