Suppose that F1 4 kN Determine the magnitude of the resulta

Suppose that F_1 = 4 kN. Determine the magnitude of the resultant force F_R = F_1 + F_2. Express your answer to three significant figures and include the appropriate units. Determine the direction of the resultant force, measured clockwise from the positive u axis. Express your answer using three significant figures.

Solution

Resolving F2 along u axes -
F2 cos (theta).
Where theta is angle between F2 and u = 30⁰
Therefore, F2 cos (theta) = 6k N * cos(30) =
F2 along u axes = 5.196k N

F2 acting perpendicular to u axes =  F2 sin (theta)
F2 sin (theta) =  6k N * sin (30)
F2 sin (theta) = 3k N

Now, angle between v axes and force perpendicular to u axes = (180 - 75) - 90 = 15⁰

Resolving F2 along v axes =  F2 sin (theta)  * cos (15^o)
Resolving F2 along v axes = 3k N * cos (15^o)
Resolving F2 along v axes = 2.898 k N

adding both the forces of u and v axes = 8.094 kn