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

Answer:-

Given:

Sum of magnitudes of two forces = 18 N

Magnitude of resultant force (R) = 12 N

Angle between Resultant and smaller force = 90°.

Let the magnitude of first force(small force) be A N.

Then the magnitude of other force (small force) will be (18 - A) N.

According to the question,

→ A = √(R + 18 - A + 2 * R * (18 - A) * cos 90°

→ A = √(12 + 18 - A)

On squaring both sides we get,

→ A² = 30 - A

→ A² + A - 30 = 0

→ A² + 6A - 5A - 30 = 0

→ A(A + 6) - 5(A + 6) = 0

→ (A - 5)(A + 6) = 0

• A - 5 = 0

→ A = 5 N

• A + 6 = 0

→ A = - 6 N

(Magnitude of force cannot be negative. So Positive value is taken. i.e., 5 N)

Hence,

• Magnitude of 1st force = A = 5 N.

• Magnitude of 2nd force = 18 - A = 18 - 5 = 13 N