The magnitudes of the four displacement vectors shown in the drawing are A = 19.
ID: 2124833 • Letter: T
Question
The magnitudes of the four displacement vectors shown in the drawing are A = 19.0 m, B = 11.0 m, C = 12.0 m, andD = 20.0 m. Determine the magnitude and directional angle for the resultant that occurs when these vectors are added together. magnitude m directional angle magnitude m directional angle
The magnitudes of the four displacement vectors shown in the drawing are A = 19.0 m, B = 11.0 m, C = 12.0 m, andD = 20.0 m. Determine the magnitude and directional angle for the resultant that occurs when these vectors are added together. The magnitudes of the four displacement vectors shown in the drawing are A = 19.0 m, B = 11.0 m, C = 12.0 m, and D = 20.0 m. Determine the magnitude and directional angle for the resultant that occurs when these vectors are added together.
Explanation / Answer
the magnitude of the resultant is sqrt[x component^2 + y component^2]
angle of resultant is given by tan(theta)=ycomponent/x component
let's see how it works in this case:
x component of vector A = - 19 cos20=-17.85
x component of vector B=0
x component of vector C=-12 cos 35 =-9.83
x component of vector D=20cos 50=12.86
total x component = -14.82
y component of A = 17 sin 20=6.49
y component of B=11
y component of C=-12 sin35 =-6.88
y component of D=-20sin50=-15.32
total y component = -4.71
magnitude = sqrt[(-14.82)^2+(-4.71)^2] = 15.55
the vector is in the third quadrant, and makes an angle with the -x axis given by:
tan(theta)=-4.71/-14.82
theta = 180 + 17.63 = 197.63
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