An engineer pulls a control handle to operate a machine. The handle is attached at the upper end of a rigid shaft, at $D$. The lower end of the shaft is pinned at $A$. A nylon rope joins to the shaft at $B$, and is secured at $C$. In a separate test, it was found that the rope stretched by 1% when a tensile force of $100$ $N$ was applied. The engineer pulls with a force $F = 112$ $N$. How far does point $D$ of the handle move ? Dimensions: $AB = 701$ $mm$, $BC = 1029$ $mm$, and $BD = 218$ $mm$.

$mm$