An overhead door, with height h$=30$ft and weight W$=800$lb$,$ consists of two identical sections

hinged at C$.$ The roller at A moves along a horizontal guide, whereas the roller at B and D$,$ 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 k if the roller at A is to strike the left end of the horizontal

guide with a maximum speed of $1\mathrm{.}5$ft$//$sec after the door is released from rest in the fully open

position.