Question

Two forces with magnitudes of 150 and 100 pounds act on an object at angles of 30° and 120°, 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

Answer:

Resultant = 180.27 pounds

direction  is  63.69 degrees

Step-by-step explanation:

We  have to resolve the x and y component of both forces with respect to given angles

Fx = 150cos30 +100cos120

    = 150(0.866)+100(-0.5) =129.9-50=79.9 pounds

and

Fy= 150sin30+100sin120

   = 150(0.5) +100(0.866)= 75+ 86.6 =161.6 pounds

Magnitude of the resultant is = $\sqrt{Fx^2+Fy^2}$

                                                 =$\sqrt{(79.9)^2+(161.6)^2}$

                                                  = 180. 27 pounds

Direction of the resultant is given by  arctan($\frac{Fy}{Fx}$

                                                               arctan($\frac{161.6}{79.9}$

                                                            =63.69 degrees