-You are to make four straight-line moves over a flat desert floor, starting at
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Question
-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 (-102 m, 53 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?
-Two beetles run across flat sand, starting at the same point. Beetle 1 runs 0.53 m due east, then 0.71 m at 26o north of due east. Beetle 2 also makes two runs; the first is 1.58 m at 49o east of due north. What must be the magnitude of its second run if it is to end up at the new location of beetle 1?
Explanation / Answer
for the 1st part,
the x cordinates add up to -102
start at 20 then add b then add -20 then add -60
20+b-20-60=-102
b=-102-20+20+60= -42
bx= -42
the y cordinates add up to 53
start at 60 then add -70 then add c then add-70
60-70+c-70= 53
c=53-60+70+70
cy=133
magnitude of overall displacement = sqrt(133^2+42^2)= 139.47
angle is 180 - atan( 42/133) = 180-72.47 = 107.53 degrees relative to the positive direction of the x axis
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