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: 16c

Answer

$14.04^{\circ}$

Work Step by Step

We're given that, $\vec{a} = (3\,m)\hat{i} + (4\,m)\hat{j}$ and $\vec{b} = (5\,m)\hat{i} + (-2\,m)\hat{j}$. We can add these vectors component-wise: $\vec{a}+\vec{b} = (3\,m+5\,m)\hat{i} + (4\,m-2\,m)\hat{j} = 8\,m\,\hat{i}+2\,m\,\hat{j}$. The angle then equals: $tan^{-1}(\frac{2\,m}{8\,m}) = 14.04^{\circ}$. This is our final answer since we take the angle between the vector and $\hat{i}$ (the positive x axis) by default.
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