Virtual experiments about a walker fly: beyond the Neumann`s solution

We extend the traditional problem of calculating the traveled distance of a fly that is moving with constant speed on a straight path between two trains that are approaching one another, we found two analytical solutions for the traditional problem and we propose a generalization to the accelerated motion of the trains through a simulation. With this problem the teachers can teach some topics of basic physics as the relations between mathematical and physics, the graphical analysis and various situations on kinematics in one dimension. We show an analogy between the move of the fly and a ultrasonic wave pulse in a sensor of velocity, this show the pedagogical power of this problem.