A bullet is fired horizontally and embeds itself in a block of wood as shown in the figure below. After the impact, the block and embedded bullet slide $12$ mm and come to a stop. The mass of the bullet is $30$ g $,$ the mass of the wooden block is $10$ kg $,$ and the coefficient of kinetic friction between the block and the surface is $\backslash (\backslash$mu$\_\{$k$\}=0\mathrm{.}4\backslash ).$

a$.$ Determine the velocity of the block and embedded bullet just after the impact.

b$.$ Determine the velocity of the bullet just before the impact.