The greatest and least resultant of two forces acting at a point is `10N` and `6N`,respectively. If each 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 `…(i)
Least resultant `= A- B =6` …(ii)`
Solving (i) and (ii) we get, ` A =8 N, B=2 N.
When each force is 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 A' B' cos 90^(@))`
`=sqrt((11) ^(2) + (5) ^(2) + 2 (11) (5)0)`
=` 12 .1 N`
Let the resultant ` vec R` make an angle ` beta` with ` vec A'`then
` tan ` beta B = (B' sin 90^(@))/(A'+ B xx B' cos 90^(@))`
(5 xx 1)/(11 + 5 xx 0) = 5 /(11) = 0.4545`
`= tan 24^(@) 26'`
` beta =24^(@) 26'.