I have two engineers working on this problem.
To get them involved, I needed to rephrase the problem in terms of a baseball bat hitting a ball.
They are baseball nuts, so this got their attention. While there is a book on the physics of baseball, as far as we know nobody has considered a bat with a sliding mass (probably not legal anyway
), so they want to work on this in case they come up with a "super bat" they can use in their Sunday softball league.
Engineers are like that -- give 'em a question they don't know the answer to, and they will worry away at it for hours. BTW, summer is a quiet time in our office.
Will be back in touch when, and if, they can find an answer.
Ian.