Two forces act simultaneously on a particle. Force F1 has magnitude 8N and acts at 30∘ above the positive x-axis. A second force F2 has unknown magnitude and direction.
The resultant FR=F1+F2 is directed wholly along the positive y-axis (that is, its x-component is zero) and has magnitude 12N.
Solve the following:
a. (i) Set up the component equations for FR in terms of the unknown magnitude F2 and its direction angle θ measured from the positive x-axis.
b. (ii) Determine the numerical values of F2 and θ.
c. (iii) State fully the vector F2 in unit-vector form.