Two perpendicular forces of magnitudes and
newtons are acting on a particle. Find the value of if the resultant bisects the angle between the forces.
Remember that for two forces and
acting at a point with a resultant force of
, where makes an angle
of with and
makes an angle of with , we can apply
the following formula:
where , , and are the magnitudes of the forces.
Since the resultant bisects the angle between the two forces, then . Therefore, we can rewrite the formula as follows:
Substituting the vales of and into this equation, we can solve for :