Tow forces acting on a paritcle in opposite directions have a resultant `1 N`. If they act at right angle to each other, the resultant is `5 N`. Find the values of two forces.

Explanation

Let `F_1` and `F_2` be the two forces acting on a particle.
(i) When the forces act in opposite directions, then
`F_1-F_2=1` or `F_1=1+F_2` …(i)
(ii) When the forces act at right angle to each other then resultant force is
`F=sqrt(F_1^2+F_2^2)=5` or `F_1^2+F_2^2=25`
or `(1+F_2)^2+F_2^2=25` or `2F_2^2+2F_2-24=0`
or `F_2^2+F_2-12=0`
On solving, we get `F_2=3N` and `-4N`
From (i), `F_1=3+1=4N` or -4+1=-3N`
`:.` Value of `F_1=4N`, `F_2=3N`