Question

All the forces below are acting on the same object at the same time. Determine the resultant
force magnitude and direction. (hint: you should have two answers)
Show all your calculations
3 N north, 4 N south, 6 N north, 6 N east, 18 N east, 23 N west, 14 N north

Answer 1

consider north and south only first

3 N north, 4 N south, 6 N north, 14 N north

the north forces add up to 23N
the south forces add up to 4N

the north and south partially "cancel out" and you're left with 23N - 4N = 19N north

repeat this process with the east and west vectors

now, once you have both your N/S and your E/W vectors, you'll use the formula

\[|A| = \sqrt{Ax^{2}+Ay^{2}}\]
where |A| is the magnitude of the final direction vector, and Ax and Ay are your N/S and E/W vectors from before.

the direction should be in between the two vectors. ***for example*** if the two vectors are north and west, the final direction is northwest.