$1.$ The truss shown below is secured by a pin at A and a roller at E $.$ Length of bars $\backslash (\backslash$mathrm$\{$AF$\},\backslash$mathrm$\{$FB$\},\backslash$mathrm$\{$FE$\},\backslash$mathrm$\{$EC$\}\backslash )$ and ED is $6$ ft $.$ Three loads are applied at $\backslash (\backslash$mathrm$\{$B$\},\backslash$mathrm$\{$C$\}\backslash )$ and D as shown.

$($a$)(2$ points$)$ If $\backslash (\backslash$mathrm$\{$P$\}=21\backslash$mathrm$\{$kip$\}\backslash )$ the roller reaction at point E is: $($please show your work$)$

$($a$)$ Indeterminate

$($b$)100$ kip to the right

$($c$)100$ kip to the left

$($d$)329$ kip to the right

$($e$)0$ kip

$($f$)$ None of the above

$($b$)(3$ points$)$ If $\backslash (\backslash$mathrm$\{$P$\}=21\backslash$mathrm$\{$kip$\}\backslash ),$ determine the internal force in member FC$.$ State whether it is in tension or compression. $($Hint: Draw all necessary FBDs and equations for full credit$)($c$)(\backslash (\backslash$mathbf$\{3\}\backslash )$ points$)$ If $\backslash (\backslash$mathrm$\{$P$\}=21\backslash$mathrm$\{$kip$\}\backslash ),$ determine the internal force in member EF $.$ State whether it is in tension or compression. $($Hint: Draw all necessary FBDs and equations for full credit$)$

$($d$)(2$ points$)$ List two essential assumptions for this to be a truss.

$($e$)(3$ points$)$ How should the force P change so that member EC becomes a zero$-$force member? $($e$.$g$.$ it experiences no internal force$).($Hint: Draw all necessary FBDs and equations for full credit$)$