The maximum and the minimum value of the resultant of two forces are 15N and 7N respectively . If the magnitude of each force is increased by 1 N and these new forces act at an angle `90^(@)` to each other, find the magnitude and direction of their resultant.

Explanation

Let the magnitude of the force be P and Q .

As per given condition, P+Q= 15 N ……..(1)
and P-Q= 7 N …………(2)
By solving (1) and (2) ,we get P=11 N and Q =4 N.
When each of the two forces is increased by 1 N in magnitude , the new magnitudes are P =(11+1) =12 N and Q=(4+1) =5 N [Fig.2.13] and since the angle between these new forces is `90^(@)`,
new resultant =`sqrt(12^(2)+5^(2))=13 N`
Let the angle of inclination of the resultant with the force 12 N be `theta`.
Then, `tan theta =5/(12) or, theta = tan^(-1) 5/(12)`.
`therefore` The magnitude of the resultant is 13 N and it is inclined with the force 12 N at an angle `tan(-1) 5/(12).`