The resultant of two 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 .

Explanation

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 )`
`implies 28 = sqrt((3x)^2 + (5x )^2 + 2 (3x ) (5x ) cos 60^@ )`
`implies 28 = sqrt( 9x^2 + 25 x^2 + 15 x^2 )= 7x`
`implies x =(28 )/(7) = 4 , therefore _1 = 3 xx 4 = 12 N, F_2 = 5 xx 4 = 20 N.`