Question

Three forces with magnitudes of 75 pounds, 100 pounds, and 125 pounds act on an object at angles of 30°, 45°, and 120°, respectively, with the positive x-axis. Find the direction and magnitude of the resultant force.

Answer 1

Answer: Direction =71.33°

Magnitude = 228.49lb

Step-by-step explanation:

F1= 75cos30°I + 75sin30°=37.5sqrt3i+37.5j

F2=100cos45°+100sin45°= 50sqrt2i+50sqrt2j

F3=125cos120+125sin120=-62.5i+62.5sqrt3j

F1+F2+F3= (37.5sqrt3+50sqrt2-62.5)I +(37.5+50sqrt2+62.5sqt2)j

Direction= (37.5 +50sqrt2+62.5sqrt3)/37.5sqrt3+50sqrt2-62.5

Direction=71.33

/F1+F2+F3/=sqrt(37.5sqrt3+50sqrt2-62.5)^2+(37.5+50sqrt2+62.5sqrt3)^2

/F1 +F2+F3/=228.49lb