conservation of momentum when a bullet hits a block why momentum is conserved when a bullet hit a block horizontally even when force of bullet is acting on it and net external force is not zero ?
 A: Let's assume that this bullet + block collision takes place on Earth, where there is gravity, then the momentum of the bullet itself is not conserved, but the horizontal component of the total momentum of the system consisting of the bullet + block is conserved.
The net external force on the system consisting of the bullet + block is that of gravity $\mathbf F_\mathrm{g}$, so the total momentum $\mathbf P$ of the system satisfies
\begin{align}
  \dot{\mathbf P} = \mathbf F_\mathrm{g}
\end{align}
by Newton's Second Law.  Notice, however, that $\mathbf F_\mathrm{g}$ points only in the vertical direction.  If we take the positive vertical direction to correspond to the positive $y$-direction of a cartesian coordinate system so that the positive $x$-direction points horizontally to the right, then the force of gravity on the system can be written as
\begin{align}
  \mathbf F_\mathrm g = F_\mathrm g\hat{\mathbf y}
\end{align}
and Newton's second law becomes
\begin{align}
  \dot P_x = 0, \qquad \dot P_y = F_\mathrm g
\end{align}
In other words, the $x$-component of the total momentum of the system is conserved, while the $y$-component is not.
So when you're doing problems with this setup, you can always assume that the total momentum in the $x$-direction of the bullet + block is conserved.
A: The momentum of the combined system of the bullet + the block is conserved, assuming that there are no outside forces acting on the system (such as air resistance).
A: Momentum is an abstract reality. An object only has momentum when it moves and as long as it doesn't make contact with another object. But when an object with momentum makes contact with another object the momentum is converted into kinetic energy. That is mv = 1/2 mv^2. It is as if you integrate the momentum at the moment of impact. The integral of mv is 1/2 mv^2, which in effect states that momentum is converted to kinetic energy at the moment of impact. The question becomes, how is momentum conserved when it is converted to kinetic energy?
