Question

Chapter 03, Problem 021 An ant, crazed by the Sun on a hot Texas afternoon, darts over an xy plane scratched in the dirt. The x and y components of four consecutive darts are the folowing, au in centimeters: (25.0, 47.0). (br.-64.0), (-19.0. Су), (-81.0,-53.0) The overall displacement of the four darts has the xy components (-140, 32.0).What are (a) b and (b) cy? What are the (e) magnitude and (d) angle (counterclockwise from the positive direction of the x axis) of the overall displacement?

Answer 1

$\overrightarrow{r}=\overrightarrow{r_{1}}+\overrightarrow{r_{2}}+\overrightarrow{r_{3}}+\overrightarrow{r_{4}}$

a)

25+b_x-19-81=-140

b_x=-65 cm

b)

47-64+c_y-53=-32

c_y=38 cm

c)

r=sqrt[(-65)²+38²]=75.3 cm

d)

$\theta =tan^{-1}\left ( \frac{38}{-65} \right )=180-30.3=149.7^{o}$ Counterclockwise from +x-axis