ADDITION OF VECTORS BY COMPONENTS?

Question

The magnitudes of 4 vectors are as follows...

vector A=19m, 20 degrees north of west

vector B=11m, due north

vector C=12m, 35 degrees south of west

vector D=35m, 50 degrees south of east

What is the magnitude and directional angle of the resultant that occurs when these vectors are added together.

Thanks for your help...I'm trying to get my physics homework submitted online before Hurrican Gustav knocks out my power.

Answer 1

First, convert your directions to rational ones based on degrees measured CW from a reference line (north, for example).

Then figure all the northerly components by taking the vector times the cosine of its angle.  Figure the easterly components by using the vector times the sine of its angle.  Sum each group to get the N & E vectors of the answer.  Its magnitude will be √(N²+E²).  Its direction (in degrees CW from N) will be arctan(E/N).

Answer 2

vector A=19m, 20 degrees north of west

vector B=11m, due north

vector C=12m, 35 degrees south of west

vector D=35m, 50 degrees south of east

horizontal components

Ax = -19 cos 20 = -17.85 m

Bx = 0

Cx = -12 cos 35 = -9.83 m

Dx = 35 cos 50 = 22.50 m

Rx = Ax + Bx + Cx + Dx = -17.85 + 0 - 9.83 + 22.50

Rx = -5.18 m

vertical components

Ax = 19 sin 20 = 6.50 m

Bx = 11 m

Cx = -12 sin 35 = -6.88 m

Dx = -35 sin 50 = m

Ry= Ay + By + Cy + Dy = 6.5 + 11 - 6.88 - 26.81

Ry = -16.19

R^2 = -5.18^2 + 16.19^2 = 288.95

R = sqrt (288.95)

R = 17.0 m

direction

tan x = -16.19 / -5.18 = 3.125

x = arctan (3.125)

x = 72.2 degrees southwest