When we hit the wall by a hammer, Newton’s third law says that hammer applies force on the wall (action) and wall applies force on hammer (reaction) equal in magnitude but opposite in direction ok fine. Now my question is if we hit a tire of a bus that is full of air with the same hammer and with the same force we feel greater backward push (after striking the tire the hammer comes back with greater speed while this is not the case when we are hitting the wall) why?
In both cases and at all times, the force from the (wall/tire) on the hammer equals the force from the hammer on the (wall/tire) : total momentum must be conserved.
However, in the first case, the initial energy is dissipated in the wall (as heat and/or damage), so at the end the hammer is stopped.
In the second case the initial energy is stored as mechanical deformation (potential energy). As soon as the hammer is stopped, this energy does work on the hammer and that sends the hammer backwards. This "follow-up" doubles the momentum exchange between hammer and tire, that's what you feel different.