The sum of the magnitudes of two forces acting at a point is and the magnitude of their resultant is . If the resultant is at with a force of smaller magnitude, what are the magnitudes of forces?
Step 1. Given Data,
The sum of magnitudes of two forces is given as,
The magnitude of their resultant is 12,
Step 2. Formula Used,
The resultant force of and is
and be the two vectors.
Let the angle between the two vectors be
Let be the magnitude of the smaller force, be the magnitude of the larger force and the resultant force be .
Thus, it can be written as,
Step 3. Calculate the magnitude of Forces,
Let the magnitude of the smaller force is , the magnitude of the larger force is and the resultant force be .
As the resultant force makes with the smaller force then forms the hypotenuse of the triangle.
Thus, it can be written as,
The sum of magnitudes of two forces is given as,
Substituting the value from equation (2) in equation (1), we get
Substituting the value of in equation (1), we get
Thus, the magnitude of the forces are and .
Hence option C is the correct answer.