The resultant of two forces whose magnitudes are in the ratio 3:5 is 28N. If the angle of their inclination is 60^(@), then find the magnitude of each force.

The resultant of two forces whose magnitudes are in the ratio 3:5 is 2

1.	The resultant of two forces whose magnitudes are in the ratio 3:5 is 28N. If the angle of their inclination is 60^(@), then find the magnitude of each force.
Answer» Solution :Let`F_(1)"and " F_(2)` be the two forces. Then `F_(1)=3x, F_(2)=5x, R=28N"and"theta= 60^(0)` `R=sqrt(F_(1)^(2)+F_(2)^(2)+2F_(1)F_(2)COS theta)` `rArr28=sqrt((3x)^(2)+(5x)^(2)+2(3x)(5x)cos60^(@))` `rArr 28=sqrt(9x^(2)+25X^(2)+15x^(2))=7x` `rArrx=(28)/7=4,:. F_(1)=3xx4=12N,F_(2)=5xx4=20N`.