Virtual experiments about a walker fly: beyond the Neumann solution

We extend the traditional problem of calculating the distance of travel of a fly that is moving with constant speed along 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 mathematics and physics, the graphical analysis and various situations on kinematics in one dimension. We show an analogy between the motion of the fly and a ultrasonic wave pulse in a sensor of velocity, which indicates the pedagogical power of this problem.

motion of a fly; Neumann problem; sensor; ultrasound