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: 29


$x^2 +(y+\dfrac{g \ t^2}{2})=v_0^2 t^2$

Work Step by Step

$x^2 +(y+\dfrac{g \ t^2}{2})=(v_0 \cos \alpha)^2 t^2+(v_0 \sin \alpha)^2 t^2$ $\implies x^2 +(y+\dfrac{g \ t^2}{2})=v_0^2 t^2 ( \cos^2 \alpha+ \sin^2 \alpha)$ $\implies x^2 +(y+\dfrac{g \ t^2}{2})=v_0^2 t^2 (1)$ $\implies x^2 +(y+\dfrac{g \ t^2}{2})=v_0^2 t^2$
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