Problem $2$

Numerical Problem $(20$ points$)$: Your personal trainer wants to help you strengthen yourself by using principles of static equilibrium. They ask you to sustain the $33kg$ ball at a certain distance from the wall. You pull the ball and rope system with a force $F$ directed towards positive $x-$axis as shown in the figure. Please calculate the following parameters remembering that the free$-$body diagram $($your FBD should be made of straight lines using a ruler$)$ is worth $5$ points for each section:

Calculate the internal normal forces in $AD,AC$ and $AB$ ropes, such that you pull the ball and rope system with a $291N$ force, and the distance $\text{'}$d$\text{'}$ is $1\mathrm{.}78m.$

Calculate the pull force $F$ such that the distance $\text{'}d\text{'}$ is $1\mathrm{.}5m$ and the force in rope $AB$ is half of that in rope $AC.$ In this problem you do not have to create an exploded view, but only the FBD about point of interest $\text{'}$A$\text{'}$ to solve the system.