The spring has a stiffness $\backslash ($ k$=50\backslash$mathrm$\{$lb$\}/\backslash$mathrm$\{$ft$\}\backslash )$ and an unstretched length of $2$ ft $.$ As shown, it is confined by the plate and wall using cables so that its length is $1\mathrm{.}5$ ft $.$ A $4\mathrm{.}1-$lb block is given a speed $\backslash ($ v$\_\{$A$\}\backslash )$ when it is at $\backslash ($ A $\backslash ),$ and it slides down the incline having a coefficient of kinetic friction $\backslash (\backslash$mu$\_\{$k$\}=0\mathrm{.}2\backslash ).$ It strikes the plate and pushes it forward $0\mathrm{.}25$ ft before stopping. Neglect the mass of the plate and spring. $($Figure $1),$

Determine the speed of the block at $\backslash ($ A $\backslash ).$

Express your answer to three significant figures and include the appropriate unit