The sum of magnitudes of two forces acting at a point is 16N. If their resultant is normal to the smaller force and has a magnitude of 8N. Then the forces are:

Explanation

Let `vecF` be the resultant of two forces, `vecF_(1)` and `vecF_(2)` as shown in figure with `F_(2) gt F_(1)`
`F_(2) sin theta= F_(1)`……..(i)
`F_(2) cos theta = F=8`…….(ii)
Squaring and adding Eqs. (i) and (ii), we get
`F_(2)^(2) = F_(1)^(2) + 64`..........(iii)
Given `F_(1) + F_(2) = 16`..........(iv)
Solving Eqs. (iii) and (iv) , we get
`F_(1) = 6N` and `F_(2) = 10 N`