Asked by Rachel
The magnitudes of the four displacement vectors shown in the drawing are A = 14.0 m, B = 11.0 m, C = 12.0 m, and D = 25.0 m. Determine the (a) magnitude and (b) direction for the resultant that occurs when these vectors are added together. Specify the direction as a positive (counterclockwise) angle from the +x axis.
Angles: In quad II from the -x axis to A is 20degrees. B lies on the +y axis 0 degrees. C is in the III quad and from the -x axis the angle is 35 degrees. D is in the fourth quad and from the +x axis the angle is 50 degrees.
Angles: In quad II from the -x axis to A is 20degrees. B lies on the +y axis 0 degrees. C is in the III quad and from the -x axis the angle is 35 degrees. D is in the fourth quad and from the +x axis the angle is 50 degrees.
Answers
Answered by
Steve
In x-y coordinates,
A = (-13.156,4.788)
B = (0,11)
C = (-9.830,-6.883)
D = (16.070,-19.151
Add them all up and you get (-6.916,-21.246)
The resultant thus has magnitude
√(6.916^2 + 21.246^2) = 22.343
and direction θ where
tanθ = -21.246/-6.916 = 71.97° in QIII, or 251.97°
A = (-13.156,4.788)
B = (0,11)
C = (-9.830,-6.883)
D = (16.070,-19.151
Add them all up and you get (-6.916,-21.246)
The resultant thus has magnitude
√(6.916^2 + 21.246^2) = 22.343
and direction θ where
tanθ = -21.246/-6.916 = 71.97° in QIII, or 251.97°
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