momentum is conserved! [duplicate]

Question

my physics textbook says that If two bodies stuck together after the collision and move as a single body with a common velocity then the collision is said to be perfectly inelastic collision.

Consider an example,when a mud ball is thrown on a wall, both of them (ball and wall) do not move but both of them stuck together. will this collision be considered perfectly inelastic? Further my teacher said that momentum is conserved in each kind of collision, but i don't see any momentum after the collision of mud ball and wall, hence two cases arises:

1. My teacher is wrong

2. The system is non-isolated (law of conservation of momentum is applicable to an isolated system)

Where the things went wrong?

Answer 1

The collision is inelastic. You say that you don't see any momentum, but you actually mean that you do not see any speed. The momentum is $p=mv$, and so you have to take into account the mass of the final system. By momentum conservation, if $m$ is the mass of the mud and $M$ the mass of the rest of the system (wall plus the earth to which it is fixed!)

$$m v_{mud} = (m+M)v_{system}$$ and so the final speed of the system is $$v_{system}=\frac{m}{m+M} v_{mud} \approx 0$$ since $M$ is huge compared to $m$. By $v_{system}$ I mean the final velocity of the system composed by the wall, the Earth and the mud.