a $3\mathrm{.}27$ g marble is fired vertically upward using a spring gun. the spring must be compressed $8\mathrm{.}76$ cm if the marble is to just reach a target $19\mathrm{.}2$ m above the marble's position on the compressed spring. $($a$)$ what is the change in the gravitational potential energy of the marble$-$Earth system during the $19\mathrm{.}2$ m ascent? $($b$)$ what is the change in the elastic potential energy of the spring during its launch of the marble? $($c$)$ what is the spring constant of the spring?