Question

Find the vector sum of the two forces : F1 = 25N 62(degrees) above x-axis. F2 = 25N 62(degrees) below the x-axis.

Answer 1

50N 62 degrees above x-axis

Answer 2

Add all the vertical, and horizontal components. In polar co-ordinates, 62 degrees above the x-axis remains 62 degrees, and 62 degrees below the x-axis becomes (360-62=298) degrees.

\[F_V=F\times sin(\theta)\]\[F_H=F \times cos(\theta)\]
You'll end up with two vectors in the vertical direction, and two vectors in the horizontal direction. You then add the vertical ones, and horizontal ones separately, and in most cases you'll be able to make a right-angled triangle. The hypotenuse will tell you the magnitude of the vector, and you could also work out the direction with trigonometry. This case is slightly different however, you should see exactly how later on!