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Q1E

Expert-verifiedFound in: Page 121

Book edition
1st Edition

Author(s)
Paul Peter Urone

Pages
1272 pages

ISBN
9781938168000

**Find the following for path A in Figure,**

**(a) the total distance traveled, and **

**(b) the magnitude and direction of the displacement from start to finish.**

**The various lines represent paths taken by different people walking in a city. All blocks are **120 m** on a side.**

a. The total distance traveled is 480 m.

b. The magnitude and direction of the displacement from start to finish is 379.4 m & $71.{6}^{\xb0}NE$

**A vector is a quantity that has both magnitude and direction. Displacement, velocity, force, torque, and other vector quantities are examples.**

a) Block = 120 m

For path A, the total distance traveled is:

$=4\mathrm{blocks}\phantom{\rule{0ex}{0ex}}=4\times 120\mathrm{m}\phantom{\rule{0ex}{0ex}}=480\mathrm{m}$

Therefore the total distance traveled by path A is 480 m.

**b) The magnitude of the displacement from start to finish is:**

$\left|\stackrel{\rightharpoonup}{d}\right|{=}\sqrt{{{d}_{x}}^{2}+{{d}_{y}}^{2}}{=}\sqrt{{\left(1block\right)}^{2}+{\left(3block\right)}^{2}}$

$\begin{array}{rcl}\left|\stackrel{\rightharpoonup}{\mathrm{d}}\right|& =& \sqrt{1+9}\mathrm{blocks}\\ & =& \sqrt{10}\mathrm{blocks}\\ & =& \sqrt{10}\times 120\mathrm{m}\\ & =& 3.162\times 120\mathrm{m}\\ & =& 379.4\mathrm{m}\end{array}$

The direction of the displacement:

$\begin{array}{rcl}\mathrm{\theta}& =& {\mathrm{tan}}^{-1}\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)\\ & =& {\mathrm{tan}}^{-1}\frac{3\mathrm{block}}{1\mathrm{block}}\\ & =& {\mathrm{tan}}^{-1}\left(3\right)\\ & =& 71.{6}^{\xb0}\mathrm{NE}\end{array}$

Therefore the magnitude and direction of the displacement from start to finish is 379.4 m & $71.{6}^{\xb0}NE$

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