Question

A force F1 of magnitude 6.00 units acts at the origin in a direction 30.0 above the positive x axis. A second force F2 of magnitude 5.00 units acts at the origin in the direction of the positive y axis. Find graphically the magnitude and direction of the resultant force F1 + F2

Answer 1

F1 = 6*cos(30) i + 6*sin(30) j = 5.20 i + 3 j 
F2 = 0 i + 5 j 

R = F1 + F2 
Add the 'i's together (x direction) and the 'j's together (y direction) 
R = (5.20 + 0) i + (3 + 5) j = 5.2 i + 8 j 

Magnitude: 
||R|| = √(5.2^2 + 8 ^2) = √91 = 9.54 

Direction: 
Θ = atan ( Rj / Ri ) = atan( 8 / 5.2 ) = 57.0⁰