The greatest and least resultant of two forces acting at a point is 10 N and 6 N respectively. If each force is increased by 3 N, find the resultant of new forces when acting at a point at an angle of `90^(@)` with each other.

Explanation

Let A and B be the two forces.
`:.` Greatest resultant `=A+B=10 " "..(i)`
Least resultant `=A-B=6 " "...(ii)`
Solving (i) and (ii) we get `A=8N, B=2 N`
When each force in increased by 3 N, then `A.=A+3=8+3=11 N`
`B.=B+3=2+3=5 N, theta=90^(@)`
`:. R.= sqrt(A^(.2)+B^(.2)+2A.B. cos 90^(@))= sqrt((11)^(2)+(5)^(2)+2(11)(5)0)=12.1 N`
Let the resultant `vecR` make an angle `beta` with `vecA` then
`"tan" beta=(B. sin 90^(@))/(A.+B. cos 90^(@))=(5xx1)/(11+5xx0)=(5)/(11)=0.4545=tan 24^(@)26.`
`beta=24^(@)26.`