A spring loaded ballistic pendulum gun requires an increasing force to load. When loading a ball of mass $0\mathrm{.}044$ kg$,$ the spring is compressed $8\mathrm{.}00$ cm$,$ the gun is fully loaded, and the force required is $80\mathrm{.}0$ N$.$ Calculate the work required to load the gun. Calculate the speed of the ball as it leaves the gun. How high would the ball rise if it was fired vertically upward $($neglect friction$).$