Question

A 110 n force and a 55 n force both act on an object point p. the 110 n force acts at 90 degrees. the 55 n force acts at 0 degrees. what is the magnitude and direction of the resultant force?

Answer 1

To determine the magnitude and the direction of the resultant force, we assume that the forces are in XY coordinate plane and the angles that are given are from  the x axis.
 
The 110 N force is said to act at 90 deg which means it is along the Y axis. The 55 N force is said to act at 0 deg which means it is along the X axis. so, a right angle is made by the two forces. Thus, the

X component of the resultant force = 55 N 
Y component of the resultant force = 110 N 
Magnitude of the resultant force would be calculated as follows:
R = √(Fx^2 + Fy^2)
R = √(55^2 + 110^2)  
R = √(15125) 
R = 123 N 
The resultant force  would have its terminal side in the x-axis. We calculate angle θ as follows:
 
tan θ = Fy/Fx 
tan θ = 110 N /55 N = 2
θ = arctan(2) 
θ = 63.4 degrees
Therefore, the magnitude of the resultant force is 123 N and the direction would be at an angle of 63.4 degrees.