Question

The forces acts at a point
1 20N inclined at 30deg towards north of east
2 25N towards north
3 30N inclined at 45deg towards north of west
4 35N inclined at 40deg towards south of west
Find the magnitude and direction of the resultant force.

Answer 1

Let us resolve the components of forces along the positive x axis = East... and  positive y axis ie., North..

   F_x = 20 Cos 30⁰  - 30 Cos 45⁰ - 35 Cos 40⁰  Newtons
         =  - 30.704 Newtons in the direction of  West...

  F_y =  25 + 30 Cos (90-45)  - 35 Cos (90-40)
          = 23.715  Newtons  towards  North.

Resultant is =  [tex]\sqrt{F_x^2+F_y^2}=  38.796  Newtons
direction is :  Ф deg. North of West
     Tan Ф =  | F_y /  F_x | =  23.715 / 30.704 = 37.68 deg.