An egg is dropped from a third$-$floor window and lands on a foam$-$rubber pad without breaking. The acceleration of gravity is $9\mathrm{.}81$ m$/$s $2.$ If a $56\mathrm{.}2$ g egg falls $14\mathrm{.}8$ m from rest and the $7\mathrm{.}84$ cm thick foam pad stops it in $6\mathrm{.}50$ ms$,$ by how much is the pad compressed? Assume constant upward acceleration as the egg compresses the foam$-$rubber pad. $($Assume that the potential energy that the egg gains while the pad is being compressed is negligible.$)$ Answer in units of m$.$