A $10\mathrm{.}0-$g bullet is fired into, and embeds itself in$,$ a $1\mathrm{.}70-$kg block attached to a spring with a force constant of $22\mathrm{.}1$ N$/$m and whose mass is negligible. How far is the spring compressed if the bullet has a speed of $300$ m$/$s just before it strikes the block and the block slides on a frictionless surface?  Use conservation of momentum in this problem because of the inelastic collision between the bullet and block.