Ballistic Spring

A bullet of mass $m$ and velocity $\vec{v}_0$ hits a block of mass $M$ that is sitting on a frictionless table, at rest, attached to a spring of mass $k$ as shown. At $t = 0$ the bullet enters the block and ``sticks'' (as in the ballistic pendulum). At this instant, the block is in its equilibrium position, which you should consider to be $x = 0$.

a) The initial position of the bullet and block combination is $x = 0$, as noted. Find the initial velocity of the block and bullet immediately after the collision;

b) What is the total energy of the bullet/block/spring system immediately after the collision? How much energy was lost to heat?

c) Find the greatest distance $x$ that the spring will compress before the bullet/block come to rest.