In a "worst$-$case" design scenario, a $2000$ kg elevator with broken cables is falling at $4\mathrm{.}00$ m$/$s when it first contacts a cushioning spring at the bottom of the shaft. The spring is supposed to stop the elevator, compressing $2\mathrm{.}00$ m as it does so$.$ Spring coefficient is $10\mathrm{.}6$ kN$/$m$.$ During the motion a safety clamp applies a constant $17000-$N frictional force to the elevator. What is the speed of the elevator after it has moved downward $1\mathrm{.}00$ m from the point where it first contacts a spring?