Bullet problem (Dynamics)

∵ M1.V1 + M2.V2 = ( M1 + M2 ) V

∴120 × 390 + 3000 × 0 = ( 120 + 3000 ) V

∴46800 = 3120 V

∴V = 15 m\sec

combined velocity= m1v1/(m1+m2) taking into account that initial momentum = final momentum

Looking at the question, "given that the momentum of the system doesn't change due to impact" hints us that the problem will be about conservation of momentum (hence, treating the bullet-wood-earth system as a closed one). Lets look into that:

$p_0 = p_1$ , where $p_0$ is momentum before the impact and $p_1$ - momentum after the bullet had hit the block.

$p_0 = v_{bullet}\cdot m_{bullet} + v_{wood}\cdot m_{wood}$ , but we know that the wooden block didn't move before the impact, so: $p_0 = v_{bullet}\cdot m_{bullet}$ .

$p_1 = v_{bullet2} \cdot m_{bullet} + v_{wood2} \cdot m_{wood}$ , but since the bullet will go into the wooden block we know that the bullet and the block will travel at the same velocity, hence: $v_{bullet2} = v_{wood2} = v$ .

$p_1 = v\cdot (m_{bullet}+m_{wood})$

$p_0 = p_1$ -> $v_{bullet}\cdot m_{bullet} = v\cdot (m_{bullet}+m_{wood}$ -> $v = \boxed {\frac{v_{bullet}\cdot m_{bullet}}{m_{bullet}+m_{wood}}}$

Plugging in the values we get: $v = \boxed{15}(m/s)$