The resultant of two forces whose magnitudes are in the ratio 3:5 is 28 N. 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 28 N. 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 = 28 N` and `theta = 60^(@)` `R = sqrt(F_(1)^(2) + F_(2)^(2) + 2F_(1)F_(2) cos theta)` `rArr 28 = sqrt((3x)^(2) + (5x)^(2) + 2(3x)(5x)cos 60^(@))` `rArr 28 = sqrt(9X^(2) + 25x^(2) + 15x^(2)) = 7x` `rArr x = (28)/(7) = 4` `therefore F_(1) = 3 xx = 12N, F_(2) = 5 xx 4 = 20 N`.