STEP 1:Visualize
the problem...(a sketch is always a
good idea)
Here
I chose to draw the vectors along the X & Y axes. I could have
drawn them anywhere, but using the axes will save me busywork later on.
STEP 2: Find the
X and Y coordinates of each vector...(I call the one pointing up "A" and
the other "B")
Ax=0
Ay=1
Bx=1
By=0
Now you see why I chose to draw the vectors on the axes! That step was easy!
STEP 3: Add the vectors...
Ax+Bx = 0+1 = 1
Ay+By = 1+0 = 1
STEP 4: Use the Phytagorean Theorem to find the resulting force...
1² + 1² = resultant²
so resultant = sqrt(2) = 1.42 units
At what angle does this force act?
Look again at the drawing... hopefully your common sense
is screaming at you...
The blue
line is half way between the two original vectors.
Can we prove this?
We know that the X component =1 and that the Y component
= 1. To find the angle in degrees above the +X axis, we can use the
tangent function...
tanq = opposite side/ adjacent
side
q = 1/tan(opp/adj) = 1/tan(1/1) = 45° Hopefully this was your common sense answer too!
NOTE: On many calculators, to get the 1/tan to happen, you would hit "shift" or "inv" or maybe "2nd". I suggest you check it out on your calculator. Test it with this: the inverse tangent of 1 is 45.