Answer:
Magnitude: 121.35 pounds
Direction: 21.64°
Explanation:
1) Decompose each force into its x - y components.
2) Force 1, F1: 140 pounds at angle of 30°
x-component: F1,x
F1, x = F1 *cos(30°) = 140 pounds * cos(30°) = 121.24 pounds
y-component: F1,y
F1,y = F1 * sin(30°) = 140 pounds * sin(30°) = 70 pounds.
3) Force 2, F2: 75 poounds at 150°
x-component: F2,x
F2,x = F2 * cos(150°) = 75 pounds * cos(150°) = - 64.95 pounds
y-component: F2,y
F2,y = F2 * sin(150°) = 75 pounds * sin(150°) = 37.5 pounds
4) Resultant Force, Fr
x-component: Fr,x
Fr,x = F1,x + F2,x = 121.24 pounds - 64.95 pounds = 56.29 pounds
y-component: Fr,y
Fr,y = F1,y + F2,y = 70 pounds + 37.5 pounds = 107.5 pounds
4.1) magnitude
|Fr| = √ [ (56.29 pouns)^2 + (107.5 pounds)^2 ] = 121.35 pounds.
4.2) direction
tan(α) = Fr,y / Fr,3 = 56.29 pounds / 107.5 pouns = 0.5236
=> α = arctan(0.5236) = 27.64 °
