Question

use graphical methods to solve this problem. you may assume data taken from the graph is accurate to three digits. find the following for path a in the figure below. 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 (in m) (b) the magnitude (in m) and direction (in degrees north of east) of the displacement from start to finish magnitude m direction ° north of east

Explanation:

Step1: Count blocks for distance

Path A moves 3 blocks north and 3 blocks east. Each block is 120 m.

Step2: Calculate total distance

The total number of blocks is $3 + 3=6$. So the total distance $d$ is $d = 6\times120=720$ m.

Step3: Calculate displacement magnitude

The displacement forms the hypotenuse of a right - triangle with legs of length $x = 3\times120$ m and $y = 3\times120$ m. Using the Pythagorean theorem $D=\sqrt{x^{2}+y^{2}}$. Here $x = y=360$ m, so $D=\sqrt{360^{2}+360^{2}}=\sqrt{2\times360^{2}} = 360\sqrt{2}\approx509$ m.

Step4: Calculate displacement direction

The direction $\theta$ of the displacement is given by $\tan\theta=\frac{y}{x}$. Since $x = y$, $\tan\theta = 1$, so $\theta = 45^{\circ}$ north of east.

Answer:

(a) 720
(b) magnitude: 509
direction: 45