F1 is a force of 5 N pulling an object south and F2 is a force of 3 N pulling an object in the compass direction of N 40 degrees E. Find the magnitude of the resultant vector.

Question

Extra note: I'm having some trouble when it comes to modeling what's going on in the question. Will F2 approach F1 as F1 heads south and F2 heads N 40 E (so each object starts at a different point), or should I draw a line 5 Newtons to the South then extend it by 3 Newtons in the N40E direction from that point? Thank you very much.

Answer 1

Using "tail-to-tip" addition of vectors helps visualization.

Yes the vectors start at the same point, yet for the sake of calculation the F2 can be translated down until its tail is at the tip (arrow) of F1.

The angle between F1 and F2 is 50°. (Draw a diagram!)

Use the Law of Cosines to determine the magnitude of the resultant vector.

Use the Law of Sines to determine the direction (angle).

Answer 2

I think modelling is the toughest part of this problem. You have two vectors going in two completely different directions but starting from the same central point. Unfortunately, not something I can draw on here - feel free to set up a call if you can't figure it out based on my description. The resultant vector, which is what you are calculating, is somewhere in the middle. Figure out the angle to either the horizontal or the vertical, whichever is easiest for you. I'm going to do it to the vertical (40 degrees).

You can figure out the resultant vector by adding the x component of F2 (3Nsin40) to the x component of F1 (0 N) and the y component of F2 (3Ncos40) to the y component of F1 (-5 N). The resultant vector will be (3Nsin40, 3Ncos40-5N) or (1.93, -2.70). The magnitude of this vector will be sqrt((1.93)^2+(-2.70)^2)), or 3.32 N.

Let me know if this makes sense.