Question

A force of magnitude 100 N is directed west, and a second force of magnitude 200 N is directed 300 east of north. Find the magnitude and direction of the resultant of these two vectors.

Answer 1

The coordinates of the first force are:

$$\mathbf{F}_1 = (-100, 0)$$

The coordinates of the second force are:

$$\mathbf{F}_2 =200\times (\sin30\degree, \cos30\degree) = (100,100\sqrt3)$$

Their resultant will be:

$$\mathbf{F} = \mathbf{F}_1 + \mathbf{F}_2 =(-100+100,0+100\sqrt3) = (0,100\sqrt3)$$

Answer. $(0,100\sqrt3)$.