The sum of magnitude of two forces is 18 N and the magnitude of their resultant is 12 N.If the resultant makes an angle of 90degree with the smaller force,then find the magnitude of the forces.
the question does not make sense..the resultant vector is always longer than the two vectors because it is formed by the 90degrees intersection of the smaller forces!!!..so how come the resultant vector form a 90degree with another smaller vector??? the smaller vectors should form a 90degrees...
To find the magnitude of the forces, we can start by drawing a diagram.
Let's denote the magnitude of the smaller force as F1 and the magnitude of the larger force as F2.
Given information:
The sum of the magnitudes of the two forces is 18 N.
F1 + F2 = 18 (equation 1)
The magnitude of the resultant force is 12 N.
The resultant force makes an angle of 90 degrees with the smaller force.
Now, let's use some trigonometry to relate the magnitudes of the forces and the angle between them.
In a right triangle, the tangent of an angle is equal to the ratio of the lengths of the side opposite the angle to the side adjacent to the angle.
tan(90 degrees) = opposite side / adjacent side
Since the resultant force makes an angle of 90 degrees with the smaller force, we have:
tan(90 degrees) = F2 / F1
Since tan(90 degrees) is undefined, this tells us that F2 = 0.
Now, substitute F2 = 0 into equation 1:
F1 + 0 = 18
Therefore, F1 = 18 N.
Since F2 = 0, the magnitude of the larger force is 0 N.
Hence, the magnitude of the smaller force is 18 N and the magnitude of the larger force is 0 N.