Four forces act. Point the first, 500 lbs, acts due south. The second, 50 lbs, acts due west. The third, 400 lbs, acts due north, and the fourth, 100 lbs, acts due east. What is the magnitude and direction of the resultant?
Lets resolve the forces in horizontal and vertical direction:
Along horizontal direction: 50 lbs (due west) and 100 lbs (due east):
Net force, Fx = 50 lbs (due East)
since forces in opposite direction will cancel each other.
Similarly, along the vertical direction: 500 lbs (due South) and 400 lbs (due North)
Net force, Fy = 100 lbs (due South)
Resultant force = `sqrt(Fx^2 + Fy^2) = sqrt (50^2 + 100^2) = 111.8 lbs`
and the direction: `tan^(-1) (Fy)/(Fx) = tan^(-1) 100/50 = 63.44 degrees`
and the direction is w.r.t. horizontal. Resultant force is in South-East direction.
Hope this helps.