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Word problem, help me please.

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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.
asked Jul 30, 2014 in TRIGONOMETRY by Tdog79 Pupil

1 Answer

0 votes

Given

First force F1 =200 N

Second force,F2 =100 N

θ1 =60°

θ2 =17

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°

 

answered Jul 30, 2014 by bradely Mentor

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