A 0.001 kg bullet is fired from a gun and lodges inside a wooden block of mass 0.2 kg. The block and bullet then slide on a rough floor with a coefficient of kinetic friction μk = 0.4 before coming to rest after sliding a distance of 3 m.

Compare KE_initial, the initial kinetic energy of the bullet, with W_friction, the macroscopic work done by the frictional force between the block and the floor in stopping the block.

Not sure on this but, is KEi greater than W_friction because it is positive while w_friction is negative?

The initial velocity of the bullet was:

And this is the question I'm most stuck on. Thanks!

Only idea I could think of was setting the KE_initial equal to W_friction but I doubt that's write as I got 68.79 m/s which is wrong as the answer is supposed to be 975 m/s.

Use first the principle of conservation of momentum.

mu + MU = mv + MV

m being the mass of bullet,
u being initial velocity of bullet,
M being mass of block
U being initial velocity of block,
v being final velocity of bullet,
V being final velocity of block.

U = 0,
v = V

Then, find the work done by friction, to get v the common speed of the block and bullet.

Then use this value with your momentum equation to get u.