Question

Given two component vectors, solve for the resultant vector. Use pythagorom theorm to find the hypotenuse and use inverse (arc) tangent to solve for the angle

1. x=-.75 y=-1.25
2. x=20000 y=14000

Answer 1

\[\Large\rm \vec x=-.75,\qquad \vec y=-1.25\]
\[\Large\rm R=\sqrt{(-.75)^2+(-1.25)^2}\approx1.46\]
\[\Large\rm \theta=\arctan\left(\frac{-1.25}{-.75}\right)\approx 59^o\]This angle is in the first quadrant.
We want the angle in the third quadrant (see how both our x and y components are negative?)
\(\Large\rm 59+180=239^o\)

Answer 2

What'd you end up with on the first one? :d
anything like this?

Answer 3

well i didn't really understand when u add or subtract 180?

Answer 4

i understand whre u got r from and the 59

Answer 5

Arctangent, in order to be a function, has it's range restricted to these two quadrants.

When we use the arctangent function, it will give us an angle between -90 degrees and 90 degrees.

That's what's happening in our problem.