Question

A force F1 of magnitude 6.00 units acts at the origin in a direction 30.0 above the positive x axis. A second force F2 of magnitude 5.00 units acts at the origin in the direction of the positive y axis. Find graphically the magnitude and direction of the resultant force F1 + F2

Answer 1

Just use vector addition. Find the components of each. The components of F1 are <6cos30,6sin30> which equals F1=<13/3,5/2> . Then To find the components of F2 you do the same thing and you get <5cos90,5sin90> and that gives you F2=<0,5>. Then you add them together and get <13/3,15/2>.
You use the formula for the magnitude \[\sqrt{(13/3)^{2}+(15/2)^{2}}\]
So you get that all that junk is equal to about 26/3 for the magnitude.
Now to find the direction you use the components so you set up your right triangle and if you know what you are doing you should know that the angle = \[\tan^{-1} (y component/x component)\]
When you calculate that out you get 60 as the angle so there you have it.
Magnitude = 26/3 Angle = 60 degrees