Body motion in a resistive medium: an exactly solvable model

We introduce and solve in closed form, using momentum and kinetic energy ba lance, a simplified microscopic model of a body propagating in a one dimens ional resistive medium. For a whole family of collisions with varying degre e of inelasticities, we find that the effective resistive force on the movi ng body is opposite to and proportional to the square of the body's velocit y.