I understand that this has been answered, but I cant follow it. My apologies, physics is a realm I want to understand but it doesn't come naturally and I have no High school physics background just 1st yr Engineering physics. (passed with supps.) A particle is projected vertically upward in a constant gravitational field with an initial speed v0 . Show that if there is a retarding force proportional to the square of the instantaneous speed, the speed of the particle when it returns to the initial position is 2. Relevant equations N. 2nd Law 3. The attempt at a solution I understand that if we first solve for the way up the boundary limit for the start is v0 and at the top acceleration must be zero which is equivalent to the equation is With boundary conditions of v0 and (I think...) once I intergrate this that gives me the initial condition for the way down, right? intergrating do I * by exp. to remove the ln? e^x=e^(-1/2kg)(1+kv^2)/(1+kv0^2) I don't think my boundary conditions are correct..... my point is what do I do from here?