collision - Is momentum conserved in this situation?

Suppose we have object A , which has momentum mv. Then it elastically collides with a wall, so it's momentum now -mv, So how is momentum conserved here ?

Answer

object A has it's momentum change by $\Delta p_{A} = -2m_A v_A$. This means that the wall must gain momentum $\Delta p_{wall} = +2m_A v_A$. To conserve momentum. We can calculate the change in velocity of the wall now. $\Delta v_{wall} = \Delta p_{wall}/m_{wall} = +2 \frac{m_A}{m_{wall}}v_A$. The point here is that the mass of the wall us much greater than the mass of the object $m_{wall} \gg m_A$. so we basically treat $\Delta v_{wall}$ as being zero. This is why there is an apparent breaking of conservation of momentum, but as you can see, if you take into account the momentum of the wall you'll see momentum is conserved.