1. The problem statement, all variables and given/known data A particle of mass m is placed on the inside of a smooth paraboloid of revolution whose equation is cz = x2 + y2 , where c is a constant, at a point P which is at a height H above the horizontal x-y plane. Assuming that the particle starts from rest (a) find the speed with which it reaches the vertex O, (b) express the time τ taken to travel from that height to the vertex in the form of an integral. Do not solve it. It leads to an elliptic integral which cannot be solved analytically. P.S. I am new to the forum and i posted the same post in the Classical Physics section titled Lagrangian. It contains a picture of the paraboloid 2. Relevant equations L = T-V x = rcosθ y = rsinθ 3. The attempt at a solution I cannot figure out what should be my first step. I have a basic idea on how to do this problem. I know that i have to use L = T - V. Should i change this to polar coordinates and then take the integral of T and V from h to 0?