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.
Answer
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.
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