1. An ant, crazed by the sun on a hot Texas afternoon, darts over an xy plane sc
ID: 1417123 • Letter: 1
Question
1. 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 following, all in centimeters: (25.0, 35.0), (bx, 65.0), (25.0, cy), (95.0, 70.0). The overall displacement of the four darts has the xy components (185, 25.0).
(a) What is bx?
____cm
(b) What is cy?
____cm
(c) What is the magnitude of the overall displacement?
____cm
(d) What is the angle (relative to the positive direction of the x axis) of the overall displacement?
____°
Explanation / Answer
A.
Sx = -185 = 25 + bx - 25 - 95
bx = -185 + 95 = -90 cm
B.
Sy = -25 = 35 - 65 - cy - 70
Sy = 75 cm
C.
displacement = (-185, -25)
magnitude = sqrt (185^2 + 25^2)
magnitude = 186.68 cm
D.
direction = arctan (Sy/Sx)
= arctan (25/185) = 7.696 deg
Because it's in third quadrant
direction from +x axis will be = 180 +7.696 = 187.696 deg
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