A $0\mathrm{.}5-$kg model rocket is loaded with $0\mathrm{.}8$ kg of rocket fuel. After launch, the rocket rises at a constant rate of $4$ m$/$s$,$ but the rocket fuel is dissipated at a rate of $0\mathrm{.}15$ kg$/$s$.$ Find the work done in propelling the rocket $20$ m above the ground. $($Use $9\mathrm{.}8$ m$/$s$2$ for g$.)$