You are to make four straight-line moves over a flat desert floor, starting at the origin of an xy coordinate system and ending at the xy coordinates (-165 m, 59 m). The x component and y component of your moves are the following, respectively, in meters: (20 and 60), then (bx and -70), then (-20 and cy), then (-60 and -70). What are (a) component bx and (b) component cy? What are (c) the magnitude and (d) the angle (relative to the positive direction of the x axis) of the overall displacement?

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Аноним Аноним · Answer 1 · 2019-09-23T18:44:19+02:00

(a) The sum of all the x displacements is

[tex]20+bx-20-60=bx-60[/tex]

And we know that the final x position is -165. We deduce

[tex]bx-60=-165 \iff bx = -165+60=-105[/tex]

(b) Similarly, we sum all the y displacements and we impose them to be equal to the final displacement:

[tex]60-70+cy-70=59 \iff cy = 59-60+70+70 = 139[/tex]

(c) The magnitude of the overall displacement is given by

[tex]M = \sqrt{(-165)^2+(59)^2}=\sqrt{27225+3481}=\sqrt{30706}\approx 175.23[/tex]

(d) The angle is given by

[tex]\alpha = \arctan\left(\dfrac{59}{-165}\right)+\pi \approx 2.8 \text{ radians}[/tex]