The greatest and least resultant of two forces acting at a point in 10 N and 6N respectively. If eac force is increased by 3N, 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`……..1
Least resultant`=A-B=6`……ii
Solving I and ii we get `A=8N,B=2N`
When each force is increased by 3N, then `A.=A+3=8+3=11N`
`B.=B+3=2+3=5N, theta=90^(@)`
`:.R.=sqrt(A^(.2)+B^(.2)+2A.B.cos 90^(@))=sqrt((11)^(2)+(5)^(2)+2(11)(5))=12.1N`
Let the resultant `vecR` makes 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.`