The magnitudes of the four displacement vectors shown in the drawing are A = 14.
ID: 2125807 • Letter: T
Question
The magnitudes of the four displacement vectors shown in the drawing are A = 14.0 m, B = 11.0 m, C = 13.0 m, and D = 30.0 m. A is pointing in the 2nd quadrant, with a 20.0 degree angle. B is pointing along the poitive y-axis. C is pointing in the third quadrant with a 35.5 degree angle. And D is pointing in the fourth quadrant with a 50.0 degree angle. 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.
Explanation / Answer
x component of the resultant
14cos(180 - 20) + 11cos90 + 13cos(180 + 35.5) + 30cos(360 - 50) =
14cos160 + 11cos90 + 13cos215.5 + 30cos310 = -4.45
y component of the resultant
14sin160 + 11sin90 + 13sin215.5+ 30sin310 = -14.74
magnitude of the resultant
L = ?((-4.45)
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