Answer to Question #181631 in Physics for Jack Eickholt

Question

A 5.0 kg block of wood is at rest on a horizontal frictionless table.  The x axis is parallel to the table top.  A 10 gram bullet is fired horizontally at the block along the x axis with a speed of 300 m/s and comes to a stop inside the block. What is the speed of the block plus bullet, in m/s, after the bullet becomes embedded in the block?

Answer 1

According to conservation of momentum:

$$p_i=p_f,\\\space\\ p_i=mv+M·0,\\ p_f=(M+m)u,\\\space\\ u=v\frac{m}{M+m}=0.6\text{ m/s}.$$