The greatest and least resulatant of two forces acting at a point are `25 N`, and `5 N` respectively. If each force is incresasd by `5 N`, find the resultant of two new forces acting at right angles to other.

Explanation

Let A and B be the two forces. Then
greatest resultant `=A+B=25` …(i)
Least resultant `=A-B=5` …(ii)
On solving (i) and (ii), we get
`A=15N` and `B=10N`
When each force is increased by 5N, then new forces are
`A_1=15+5=20N`
`B_1=10+5=15N`
Since the angle between new forces is `90^@`, so their resultant force is
`R=sqrt(A_1^2+B_1^2+2A_1B_1cos90^@)=sqrt(A_1^2+B_1^2)`
`=sqrt(20^2+15^2)=25N`
Let resultant `vecR` make an angle `beta` with the direction of `vecA`, then
`tanbeta=(B_1sin90^@)/(A_1+B_1cos90^@)=B_1/A_1=15/20`
`=0*75=tan36^@52^'`
or `beta=36^@52^'`