Vectors question?

Question

Two forces are applied to a tree stump to pull it out of the ground. Force vector F A has a magnitude of 2480 newtons and points 36.0° south of east, while force vector F B has a magnitude of 3160 newtons and points due south. Using the component method, find the magnitude and direction of the resultant force vector F A + vector F B that is applied to the stump. Specify the direction with respect to due east.

Answer 1

For component method, break into components using triangles or the unit circle. For unit circle, x=F*cosα and y=F*sinα. Add components together, then convert back.

So, let +x axis be going E, +y is going N.

Ax=2480*cos(-36°) Ay=2480*sin(-36°)

Bx=3160*cos(-90°) Bx=3160*sin(-90°)

So, Cx=Ax + Bx   Cy=Ay + By, (just add the numbers together)



To convert back, need magnitude and angle.

Magnitude = √(Cx² + Cy²)

and, if you remember your slope of a line formula [rise/run or (y2 -y1)/(x2-x1)=m and arctan m = angle]

So, arctan(Cy/Cx) is angle, with respect to East.