On July $4,2005,$ the NASA spacecraft Deep Impact fired a projectile onto the surface of Comet Tempel $1.$ This comet is about $9\mathrm{.}0$ kmkm across. Observations of surface debris released by the impact showed that dust with a speed as low as $1\mathrm{.}0$ m$/$sm$/$s was able to escape the comet.

How far from the comet's center will this debris be when it has lost $70\%\%$ of its initial kinetic energy at the surface?

Assuming a spherical shape, what is the mass of this comet? $($ The escape speed for an object at the surface of Earth is $11\mathrm{.}2$ km$/$skm$/$s $).$