Chapter 3, Problem 14 You are to make four straight-line moves over a flat deser

Question

Chapter 3, Problem 14

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 (-140 m, 78 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?

Explanation / Answer

(-140 m, 78 m) = (20, 60) + (bx, -70) + (-20, cy) + (-60 and -70)
so
-140 = 20 + bx - 20 - 60, so
a) bx = -80 m
78 = 60 - 70 + cy - 70, so
b) cy = 158 m
c) overall displacement = (-140 m, 78 m)
the magnitude = (1402 + 782) = 160 m
d) the angle (relative to the positive direction of the x axis) of the overall displacement

= 180 - tan-1(78/140) = 151o

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