Determine the magnitude of the resultant force and its direc

Determine the magnitude of the resultant force and its direction as measured counter clockwise from the positive x axis.

Solution

Let I and j be the unit vectors in +x and +y directions

Resolving the force in x and y directions we have

F1 = 850 N

          =850 (4/5) i - 850(3/5) j

          = 680 i - 510 j

F2 = 625 N

     = -625Cos(60) i – 625Cos(30) j

     = -312.5i – 541.27j

F3 = 750 N

     = -750Cos(45)i +750Cos(45)j

     = -530.33i+530.33j

Resultant is vector addition of all the forces

Resultant F = F1+F2+F3

                = (680-312.5-530.33)i +(-510-541.27+530.33)j

                =-162.83i -520.94j

The resultant will make angle with +x axis

          = arctan(520.94/162.83)

         = 72.64⁰

The resultant has components along –x and –y and will be in the fourth quadrant, hence the angle measured CCW with +x

= 180+72.64 = 252.64⁰