Question

How do you calculate the net force when there are multiple forces in different directions?​

Answer 1

To find $F_{net}$ we need to use vector addition and use the x and y components. First we subtract vector 2 from vector 5 which results in a vector with a  length of 3 pointing directly east, then we use the distance formula to find the length of the net force $F_{net} = \sqrt{(3)^2+(4)^2}$  which gives $F_{net} = 5$. We now have a magnitude but we also need a direction, since vector 4 and vector 5 are perpendicular. Using $\theta = \tan^{-1} (\frac{4}{3})$   where tan^-1(y/x) we get an angle of 53 degrees. The resultant force vector is 5 distance with an angle of 53 degrees north east.