Find the resultant force of the following forces which act upon a particle . (a) 30 N due east , (b) 20 N due north , (c) 50 N due west , (d) 40 N due south .

Explanation

From figure, Resultant force ,
`vec(F) = vec(F)_(1)+ vec(F)_(2) + vec(F)_(3) + vec(F)_(4)`
`= 30 hat(i) + 20 hat(j) - 50 hat(i) - 40 hat(j)`
`= - 20 hat(i) - 20 hat(j)`
`:. |vec(F)| = sqrt((-20)^(2) + (-20)^(2))`
`= 20 sqrt(2)`
`tan phi = (20)/(20) = 1`
(or) `phi = 45^(@)`