Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 3 - Kinematics in Two Dimensions; Vectors - Problems: 45

Answer

5.31$^o$ west of south.

Work Step by Step

Call east the positive x direction and north the positive y direction. Let P denote the Plane, A the Air, and G the Ground. The pair “PG”, for example, represents the plane’s motion relative to the ground. $$ \vec{v_{PG}} = \vec{v_{PA}} + \vec{v_{AG}} $$ $$(0, V) = (688 cos \theta, 688 sin \theta) km/h + (90.0 cos 45 ^{\circ}, 90.0 sin 45 ^{\circ}) km/h$$ Equate the x-components on both sides to solve for the angle of 264.69$^o$, or approximately 5.31$^o$ west of south.
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