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Q20 P

Expert-verified
Found in: Page 59

Physics For Scientists & Engineers

Book edition 9th Edition
Author(s) Raymond A. Serway, John W. Jewett
Pages 1624 pages
ISBN 9781133947271

A girl delivering newspapers covers her route by traveling $3.00$ blocks west, $6.00$ blocks north, and then $6.00$blocks east. (a) What is her resultant displacement? (b) What is the total distance she travels?

a) The resultant displacement of the girl is 5 blocks at $53.1°$ (North of East).

b) The total distance travelled by the girl is 13 blocks.

See the step by step solution

Step 1: Define distance and displacement

Displacement of a body is defined as the body moving from its rest position to another one. Distance is defined as the length of space between two points.

Step 2: (a) Find the resultant displacement

To distribute newspapers, the girl begins at point A and follows the course ABCD.

The resultant displacement

$\text{AO}=\sqrt{{\text{AD}}^{2}+{\text{OD}}^{2}}$

Now substitute $4.0$ for AD and $3.0$ for OD.

$\text{AO}=\sqrt{{4.0}^{2}+{3.0}^{2}}\phantom{\rule{0ex}{0ex}}=5\text{}$

Calculate the angle $\theta$ :

$\mathrm{tan}\theta =\frac{\text{AD}}{\text{OD}}$

Substitute 4.0 for AD and 3.0 for OD.

$\mathrm{tan}\theta =\frac{4}{3}\phantom{\rule{0ex}{0ex}}\theta ={\mathrm{tan}}^{-1}\left(\frac{4}{3}\right)\phantom{\rule{0ex}{0ex}}\theta =53.1°\text{(North of East)}$

Here, $\theta$is the direction.

Hence, the resultant displacement of the girl is 5 blocks at $53.1°$ (North of East).

Step 3: (b) Find the total distance she travelled

The total distance travelled.

$\text{D}=\text{AB}+\text{BC}+\text{CO}$

Substitute 3.0 for AB, 4.0 for BC and 6.0 for CO.

$\text{D}=3.0+4.0+6.0\phantom{\rule{0ex}{0ex}}=13\text{blocks}$

Hence, the total distance travelled by the girl is 13 blocks.