A bullet with mass $4\mathrm{.}87$ g is fired horizontally into a $2\mathrm{.}104$ kg block attached to a horizontal spring. The spring has a constant $5\mathrm{.}77$ x $10^2$ N$/$m and reaches a maximum compression of $6\mathrm{.}33$ cm$.$

$($a$)$ Find the initial speed of the bullet$-$block system.

$($b$)$ Find the speed of the bullet.