Hello! May I first please direct your attention to Walter Lewin's first Classical Mechanics lecture on Units, Dimensions and Scaling Arguments? He first carried out a dimensional analysis to determine the relation between the time taken for a ball to fall from a particular height to the height itself, the mass of the ball and gravitational acceleration. He then mentioned that the dimensional analysis could just as well have been carried out another way, leading to different results. May anyone please tell me how in this case (and in general) how one can correctly determine all the physical quantities related to the time taken for the ball to fall? Thank you very much in advance.