## Fundamentals of Physics Extended (10th Edition)

Published by Wiley

# Chapter 3 - Vectors - Problems - Page 57: 15c

#### Answer

$12.17m$

#### 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 $b_{y}\widehat {j}$ $a_x=a\times \cos \theta _{1}=10.0m\times \cos 30= 5 \sqrt 3 m;$ $b_x=10.0m\times \cos \left( \theta _{2}+\theta _{1}\right) =10.0m\times \cos \left( 105+30\right) =10.0m\times \cos 135=-5\sqrt {2}m$ $\Rightarrow r _{x}=a_{x}+bx=5\left( \sqrt {3}-\sqrt {2}\right) \approx 1.59m$ $a_y=a\times \sin \theta _{1}=10.0m\times \sin 30= 5 m;$ $b_y=10.0m\times \sin \left( \theta _{2}+\theta _{1}\right) =10.0m\times \sin \left( 105+30\right) =10.0m\times \sin 135=5\sqrt {2}m$ $\Rightarrow r _{y}=a_{y}+b_y=5\left( 1+\sqrt {2}\right) \approx 12.07m$ $r=\sqrt {r^{2}_{x}+r^{2}_{y}}\approx 12.17m$

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