To all amateur physicists - a simple physics problem

Has anyone got anywhere with this? I get stuck where I have to solve:y'' = k/y^2 (k = const).I reckon that the cunning method involves some sort of restating the problem into an orbital motion problem (Kepler + pi were my clues here), but haven't really got anywhere with this train of thought.PE

Thanks Eta - but to be honest, I don't think that's helped me very much.Here's what I remember about Kepler:1. Orbital motion - equal areas swept out in equal times.
2. Orbital period T^2 is proportional to R^3
3. Orbital period for a planet is independent of its mass.
4. Planetary orbits are generally elliptical, with the sun at one focus.Not sure how any of that helps me - the problem is two objects travelling towards one another in a straight line.I've had two ideas, but since my physics is so rusty, I haven't been able to follow them through. The first is imagining that you were moving perpendicular to the plane of the two objects so that as they came together they would appear to you to trace out a semi-circle. The second is to picture the objects as the foci of an ellipse with ever decreasing eccentricity, and to use the parametric equation for an ellipse to determine the time taken for the two masses to collide, but it hurts my head just thinking about it.PE