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: 15

Answer

x-component: $(4580 m)(cos 122.4 ^{\circ}) = -2845 m$ y-component: $(4580 m)(sin 122.4 ^{\circ}) = 3589 m$ The z-component was given as 2450 m. The magnitude of the displacement is $5190 m.$

Work Step by Step

The x component is negative and the y component is positive, because the summit is to the west of north. The angle of the displacement vector measured counterclockwise from the positive x axis is 122.4 degrees. x-component: $$(4580 m)(cos 122.4 ^{\circ}) = -2845 m$$ y-component: $$(4580 m)(sin 122.4 ^{\circ}) = 3589 m$$ The z-component was given as 2450 m. The magnitude of the displacement is obtained using the 3 components and the Pythagorean theorem, and is 5190 m.
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