Problem 1 788 N 32 985 N 53 411 N Workmen are trying to free an SUV stuck in the mud. To extricate the vehicle, they use three horizontal ropes, producing the force vec- tors shown in the figure. Find the x and y com- ponents of each of the three pulls. Sum them to determine the components of the resultant force. Then, find the magnitude and direction (as mea- sured counterclockwise from the +x-axes) of the resultant force.

The x and y components of each pulling using the given figure,

$\begin{array}{rcl}{F}_{1x}& =& F_1 \cos {\theta }_1\\ & =& \left(985 \mathrm{N}\right) \cos \left(31°\right)\\ & =& 844.31 \mathrm{N}\end{array}$

$\begin{array}{rcl}{F}_{1y}& =& F_1 \sin \theta \\ & =& \left(985 \mathrm{N}\right) \sin \left(31°\right)\\ & =& 507 \mathrm{N}\end{array}$

$\begin{array}{rcl}{F}_{2x}& =& F_2 \cos \left(90°+{\theta }_2\right)\\ & =& \left(788 \mathrm{N}\right) \cos \left(90°+32°\right)\\ & =& -417.58 \mathrm{N}\\ & & \end{array}$

$\begin{array}{rcl}{F}_{2y}& =& F_2 \sin \left(90°+{\theta }_2\right)\\ & =& \left(788 \mathrm{N}\right) \sin \left(90°+32°\right)\\ & =& 668.26 \mathrm{N}\end{array}$