Question

Two forces with magnitudes of 200 and 100 pounds act on an object at angles of 60° and 170° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.

Answer 1

First force F1 =200 N

Second force,F2 =100 N

θ1 =60°

θ2 =170°

Take Summation of Forces Horizontal and vertical

ΣFx = 200cos60° - 100cos(180-170°)

      =200cos60° - 100cos(10°)

      = 1.519 N
ΣFy = 200sin60° + 100sin(180-170°)

      = 200sin60° + 100sin10°

      = 190.57

Resultant/Magnitude
R =√[ (ΣFx)² + (ΣFy)²]

     =√[1.519²+(190.57)²]
R = 190.576 N

Direction of resultant force

θ =arctan [ΣFy / ΣFx]
θ =89.54°