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: 1

Answer

302 km, 193$^o$ (i.e., 13$^o$ south of west).

Work Step by Step

Add the displacements using the components method. The two vectors point at 180 degrees and 225 degrees, measured counterclockwise from east. x-component: $(225 km)(cos 180^{\circ}) + (98 km)(cos 225 ^{\circ}) = -294.3 km$ y-component: $(225 km)(sin 180 ^{\circ}) + (98 km)(sin 225 ^{\circ}) = -69.3 km$ Use the Pythagorean theorem 3.4a to find the magnitude of the overall vector, and the definition of tangent, equation 3.4b, to find the angle. The vector has negative x and y-components, and points down and to the left.
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