tugn boat problem The figure below shows a schematic image of four tugboats guiding an ocean liner toward its pier, with each tugboat exerting a force of $8000$ lbs in the directions indicated.

a$)$ Sketch the components of the force vectors on the hull of the ocean liner and embed the $\backslash (\backslash$mathrm$\{$x$\}-\backslash$mathrm$\{$y$\}\backslash )$ axes on it$.$

b$)$ Resolve leaving your solution in rectangular vector form, the horizontal and vertical components of a forces exerted on the Ocean liner by

i$.)$ Tugboat $1$ ii$.)$ Tugboat $2$

iii.$)$ Tugboat $3$

iv$.)$ Tugboat $4$

c$)$ Determine the resultant force $(\backslash (\backslash$boldsymbol$\{$R$\}\backslash ))$ exerted by all the four tugboats, leave your answer in rectangular vector form

d$)$ Determine the angle $\backslash (\backslash$theta $\backslash ),$ that the resultant force makes with the horizontal axis e$)$ Determine the total moment $\backslash ($ M$\_\{$o$\}^\{$R$\}\backslash )$ of the forces exerted on the hull by the four tugboats about the origin $\backslash ($ O $\backslash ).$

f$)$ Sketch and fully label the equivalent resultant force$-$couple system at the origin $\backslash ($ O $\backslash ).$

g$)$ Determine a point $\backslash (\backslash$mathrm$\{$A$\}(\backslash$mathrm$\{$x$\},\backslash$mathrm$\{$y$\})\backslash )$ on the hull of the ocean liner where a single more powerful tugboat should push to produce the same effect as the original four tugboats. $($start by sketching the location of point A$).$