Question 43408: what is the magnitude
U: magnitude 1,850, bearing 125 degrees
V: magnitude 2,960, bearing 25 degrees
W: U+V Answer by fractalier(6550) (Show Source):
You can put this solution on YOUR website! The process of adding or subtracting vectors involving breaking the pieces down into their horizontal and vertical components first...then combining like components...then changing the components into polar form...for this one we have...I use q and p for theta and phi...
Ux = U cos q = 1850 cos 125° = -1061
Uy = U sin q = 1850 sin 125° = 1515
Vx = V cos p = 2960 cos 25° = 2683
Vy = V sin p = 2960 sin 25° = 1251
now add 'em
Wx = Ux + Vx = -1061 + 2683 = 1622
Wy = Uy + Vy = 1515 + 1251 = 2766
now
r = sqrt(x^2 + y^2) and theta = arctan(y/x) so that
r = sqrt(1622^2 + 2766^2) = 3206
and theta = arctan(2766/1622) = 59.6°
and finally (whew!)
W = magnitude 3206, bearing 59.6°
Study this example carefully because I probably won't do this kind of problem again...
