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 57: 15c



Work Step by Step

$r_{x}=\left( a_{x}+b_x\right) \widehat {i}$ $r_{y}=\left( a_{y}+b_y\right) \widehat {j}$ Lets calculate $a_{x}\widehat {i}$ ,$b_{x}\widehat {i}$. ,$a_{y}\widehat {j}$ and $b_{y}\widehat {j}$ $a_x=a\times \cos \theta _{1}=10.0m\times \cos 30= 5 \sqrt 3 m;$ $b_x=10.0m\times \cos \left( \theta _{2}+\theta _{1}\right) =10.0m\times \cos \left( 105+30\right) =10.0m\times \cos 135=-5\sqrt {2}m$ $\Rightarrow r _{x}=a_{x}+bx=5\left( \sqrt {3}-\sqrt {2}\right) \approx 1.59m$ $a_y=a\times \sin \theta _{1}=10.0m\times \sin 30= 5 m;$ $b_y=10.0m\times \sin \left( \theta _{2}+\theta _{1}\right) =10.0m\times \sin \left( 105+30\right) =10.0m\times \sin 135=5\sqrt {2}m$ $\Rightarrow r _{y}=a_{y}+b_y=5\left( 1+\sqrt {2}\right) \approx 12.07m$ $r=\sqrt {r^{2}_{x}+r^{2}_{y}}\approx 12.17m$
Small 1509563490
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.