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 777: 7


$v(1,0)=-j$ (Clockwise Motion)

Work Step by Step

$v=\dfrac{dx}{dt}i+\dfrac{dy}{dt}j$ The equation of the circle is $x^2+y^2=1$ $2 x x_t+2y y_t=0$ $\implies \dfrac{dy}{dt}=\dfrac{-x}{y} \dfrac{dx}{dt}$ Since, $\dfrac{dx}{dt}=y$ $\dfrac{dy}{dt}=\dfrac{-x}{y} \times y$ So, $\dfrac{dy}{dt}=-x$ Now, $v(1,0)=\dfrac{dx}{dt}i+\dfrac{dy}{dt}j=0 i -(1) j $ So, $v(1,0)=-j$ (Clockwise Motion)
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