Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 3 - Vectors - Problems - Page 58: 22a

Answer

$(1.28m)\hat{\mathrm{i}}+(6.60m)\hat{\mathrm{j}}$

Work Step by Step

Using (3-5) for vector components, $ a_{x}=a\cos\theta$ and $ a_{y}=a\sin\theta$. Set your calculator to radians, $\vec{E}=3.73\hat{\mathrm{i}}+4.70\hat{\mathrm{j}}$ $\vec{G}=1.45\hat{\mathrm{i}}+3.73\hat{\mathrm{j}}$ Set your calculator to degrees. $\vec{F}=1.29\hat{\mathrm{i}}-4.83\hat{\mathrm{j}}$ $\vec{H}=-5.20\hat{\mathrm{i}}+3.00\hat{\mathrm{j}}$ The resultant sum of the vectors is obtained by using (3-10 to 3-12): $\vec{E}+\vec{F}+\vec{G}+\vec{H}=[(3.73+1.45+1.29-5.20)m]\hat{i}$ $+[(4.70+3.73-4.83+3.00)m]\hat{j}$ $=(1.28m)\hat{\mathrm{i}}+(6.60m)\hat{\mathrm{j}}$.
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