The final velocity of the bullet+block is 0.799 m/s
Explanation:
We can solve this problem by applying the principle of conservation of momentum: in fact, the total momentum of the bullet-block system must be conserved before and after the collision.
Mathematically, we can write:

where
m = 0.001 kg is the mass of the bullet
u = 800 m/s is the initial velocity of the bullet
M = 1 kg is the mass of the block
U = 0 is the initial velocity of the block (initially at rest)
v is the final combined velocity of the bullet and the block
Solving the equation for v, we find the final velocity:

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