Problem $2$: $(20$ points$)$ The spring has a stiffness $\backslash ($ k$=50\backslash$mathrm$\{$lb$\}/\backslash$mathrm$\{$ft$\}\backslash )$ and an unstretched length of $2$ ft $.$ The spring is confined by the plate and wall using cables so that its length is $1\mathrm{.}5$ ft $.$ A $4-$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$\}=0\mathrm{.}2\backslash ).$ If it strikes the plate and pushes it forward $0\mathrm{.}25$ ft before stopping, determine its speed at $\backslash ($ A $\backslash ).$ Neglect the mass of the plate and spring.