A particle is being acted upon by four forces of `30 N` due east , `20 N` due north , `50 N` due west and `40 N` due south. The resultant force will be

Options

A. `20sqrt(2)N, 60^(@)` South to West
B. `20sqrt(2)N, 45^(@)`, South of West
C. `20sqrt(2)N, 45^(@)`, South of East
D. `20sqrt(2), 45^(@)`, South of East

Explanation

(b) Effective force along West `(x)=(50-30)=20N`
Effective force along Sough, `(y)=40-20=20N`
Resultant `=R=sqrt(x^(2)+y^(2))=sqrt(20^(@)+20^(@))=20sqrt(2)N`
`tan theta =y/x=1=tan 45^(@)impliestheta=(pi)/4=45^(@)`