Q$4.$ An overhead door, with height $\backslash ($ h$=30\backslash )$ ft and weight $\backslash ($ W$=800\backslash$mathrm$\{$lb$\}\backslash ),$ consists of two identical sections hinged at $\backslash ($ C $\backslash ).$ The roller at $\backslash ($ A $\backslash )$ moves along a horizontal guide, whereas the roller at $\backslash ($ B $\backslash )$ and $\backslash ($ D $\backslash ),$ which are the midpoints of sections AC and CE$,$ move along a vertical guide. The door's operation is assisted by two identical springs attached to the horizontally moving rollers $($only one of the two springs is shown$).$ The springs are stretched $0\mathrm{.}25$ ft when the door is fully open. Determine the minimum value of the spring constant $\backslash ($ k $\backslash )$ if the roller at $\backslash ($ A $\backslash )$ is to strike the left end of the horizontal guide with a maximum speed of $\backslash (1\mathrm{.}5\backslash$mathrm$\{$ft$\}/\backslash$mathrm$\{$sec$\}\backslash )$ after the door is released from rest in the fully open position.