Why is momentum conserved when a ball hits a vertical wall? Almost in every book on physics, there's an example of conservation of momentum when the ball that is moving horizontally in the air, hits some massive wall. They claim that the return speed of the ball when it bounces off is the same as it was before the hit. If there were no external forces acting on the system (or their net force was zero) that would be fine. But in this case, there is a gravitational force acting on the ball, and because there is no surface underneath it, there's no normal force and therefore it doesn't "cancel out" the gravitational force. So my question is, why they say that the momentum conserved? Do they neglect the gravitational force or what? I'm quite confused.  
 A: The assumption in these problems is that the collision takes place instantaneously so that gravity has no time to change the momentum of the ball during the collision.
To see why this is makes sense, let $y$ denote the vertical direction, and notice that if the collision took some small amount of time $\delta t>0$ then the change in vertical momentum of the ball would be (by integrating both sides of Newton's second law)
$$
  \delta p_y = \int_{t_0}^{t_0+\delta t}dt \,F(t) = F(t_0)\delta t + \mathcal O(\delta t^2)
$$
so we see that as the collision time goes to zero, so does the change in momentum in the vertical direction.
A: What are you talking about! The momentum of the ball is not conserved at all. But if it is an perfectly elastic collision the kinetic energy will be conserved and then from (1/2)m(V^2)i=(1/2)m(V^2)f you have the two velocities equal in magnitude. The momentum of the ball of course changes and the change is equal to two times the initial momentum!
A: The momentum conservation principle will be valid for horizontal direction. However, for the vertical direction gravity is the external force acting so it would not be valid
A: In this case,Linear momentum is conserved only in horizontal direction.Whereas, the same is not true for vertical direction.
A: When the ball hits the vertical wall net external force remains zero due to the presence of opposite vectors which cancels out internally, and this makes linear momentum remain conserved. 
