## Fundamentals of Physics Extended (10th Edition)

Published by Wiley

# Chapter 3 - Vectors - Problems - Page 57: 14d

#### Answer

$12^{o}$ clockwise from the +x axis, or $168^{o}$ counterclockwise from the +x axis

#### Work Step by Step

The individual moves are (meters understood as units) $\vec{a}=20\vec{i} + 60\vec{j},$ $\vec{b}=b_{x}\vec{i} - 70\vec{j},$ $\vec{c}=-20\vec{i} + c_{y}\vec{j},$ $\vec{d}=-60\vec{i} -70\vec{j},$ The resultant: $\vec{r}=\vec{a}+\vec{b}+\vec{c}+\vec{d}=-140\vec{i}+30\vec{j}$ The angle $\theta$ of the resultant is $\displaystyle \tan^{-1}\frac{30m}{-140m}=-12^{o}$, which is $12^{o}$ clockwise from the +x axis, or $168^{o}$ counterclockwise from the +x axis

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