Physics - Center of Mass Question with Solution | TestHub

This is a perfectly inelastic collision where the bullet gets embedded in the block. During the collision, the total momentum of the bullet-block system is conserved, as there are no external horizontal forces.

Let $v_{bullet}$ be the initial velocity of the bullet and $V$ be the velocity of the combined system immediately after the collision. Initial momentum of the system = $m{v}_{bullet}+M(0)$ Final momentum of the system = $(m+M)V$ By conservation of momentum:$m{v}_{bullet}=(m+M)V$ Therefore, the initial velocity of the bullet is $v_{bullet}=\frac{(m+M)V}{m}$.