Question

The sum of the magnitudes of two forces acting at a point is 18 and their resultant is 12. If the
resultant makes an angle of 90° with the force of smaller magnitude, what are the magnitudes
of the forces?​

Answer 1

Let,

The magnitude of smaller force is P,

The magnitude of larger force is Q and

The resultant force is R.

As the resultant force makes 90∘

with the smaller force P then Q forms the hypotenuse of the triangle.

Thus, it can be written as,

Q^2 −P^2 =R^2

Q^2 −P^2 =(12)^2

Q^2 −P^2 =144 (1)

The sum of magnitudes of two forces is given as,

P+Q=18

Q=18−P (2)

Substituting the value from equation (2) in equation (1), we get

(18−P)^2 −P^2 =144

P=5N

Substituting the value of P in equation (1), we get

Q=18−5

=13N

Thus, the magnitude of the forces are 5N and 13N.