use graphical methods to solve this problem. you may assume data taken from the graph is accurate to three…
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
Answer
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