So I did some math starting with 100J of potential energy and summed a geometric series to see how long it would stay in the air if we had infinite time to sum

So I did some math starting with 100J of potential energy and summed a geometric series to see how long it would stay in the air if we had infinite time to sum the geometric series and it was some finite number. Then I assumed the initial velocity in the horizontal direction was 1 m/s so if we had infinite time the ball would travel some finite distance because it would bounce infinitely often and in every such bounce it would be in the air some amount of time and would travel at a speed of 1 m/s in that amount of time. But this assumes that the ball doesn't roll along the floor when it comes down and immediately bounces up as soon as it hits the floor which is unrealistic because it means I'm assuming infinite impulse on each bounce because the momentum of the ball changes and I'm assuming this takes 0 seconds. So the best I was able to do was give an upper bound on the total distance the ball would travel if the universe were to last forever. It's a lot like Zeno's arrow or is it Achilles and the tortoise.