I have been reading a paper which introduced classical mechanics concerning only one dimension. Before we get into anything about displacement and velocity, I read about dimensional analysis. There is a section of the paper which isn't very well explained and I hope someone can explain it to me, so that I can continue reading. "A film company wants to shoot the leaning tower of pisa falling. They have built a model tower. They cannot just let it drop otherwise it would look too unrealistic. Therefore they need to slow the video down so it looks more realistic by a factor t. This factor depends on mass of tower,m, the height of the tower,h, and acceleration due to gravity, g. In other words... t = C m^x h^y g^z Where C is a dimensionless constant. The dimensions = [T] = [M]^x [L]^y ([L]/[T-squared])^z We can now compare the exponents of [L], [M] and [T]. 0 = y + z 0 = x 1 = -2z While I understand what the author is attempting to do, I do not understand how we gain the above equations, and hence the following. x = 0 y = 0.5 z = -0.5 t = C (sqrt) h/g Thank you in advance. ps - I want to understand fully how we compare the exponents, get three equations and the formula.