Falling ladders is a good example which can show the key difference between mathematics and physics. A simple and seemingly acceptable mathematical model gives prediction which obviously does not agree with experience: the speed at the top of the ladder tends to infinity when the angle between the ladder and the floor tends to zero. In the mathematical world such behavior is quite legitimately. But such model obviously does not describe good physical world – the world we live in. To describe the physical world, the model needs to be upgraded. In other words, it is necessary to take some restrictions imposed by physics. Because of that restrictions, equations usually become more complicated and it's more difficult to solve them. But that model predictions better get along with observations. In this work, a simple mathematical model of falling ladders has been upgraded into two stages. In the easier case we took a fact that ladders have a mass (because they fall in the gravity field), but that mass is placed in the center of the ladder. So, the dynamics of the dot body has been used. In a more realistic case, the mass is uniformly deployed by ladders. Solid body dynamics has been used here. In both cases, for simplicity, friction was neglected. As expected, both physical models give the ultimate speed of the top of the ladder when the ladder comes to the horizontal position.