Before I write anything, I want to apologize because I have no idea how to write equations on this website. This is my first post >.< Also, thank you for helping in advance! 1. The problem statement, all variables and given/known data A baseball is thrown vertically up with speed vo and is subject to a quadratic drag with magnitude f(v) = cv2. Write down the equation of motion for the upward journey (measuring y vertically UP) and show that it can be rewritten as v(dot) = -g[1+(v/vter)2]. Use the "vdv/dx rule" to write v(dot) as vdv/dy and then solve the equation of motion by separating variables (put all terms involving v on one side and all terms involving y on the other). integrate both sides to give y in terms of v, and hence v as a function of y. Show that the baseball's maximum height is ymax = [(vter)2/2g]*ln[ [ (vter)2 + (vo)2 ] / [(vter)2] ] whew. If vo = 20m/s and the baseball has the parameters: mass m=.15kg and diameter D = 7cm, what is ymax? Compare with the value in a vacuum. 2. Relevant equations Ok... Well first, in case you didn't get it, the vdv/dx rule is just that: v(dot) = vdv/dx = (1/2)d(v2)/dx. (only in this problem we just use y instead of x.) Another formula that's important is the terminal velocity, which is vter = sqrt(mg/c) 3. The attempt at a solution Well, the first thing it asks is to write down the equation of motion. I'm a little unsure, but I think that it is : m*v(dot) = -mg - cv2 which can be rearranged: v(dot) = -g - cv2/m and substituting c/m = g/(vter)2 in... v(dot) = -g (1 + (v/vter)2) so then we use the vdv/dx rule... vdv = -g*dy*(1 + (v/vter)2) and separating variables like it said, vdv/(1 + (v/vter)2) = -gdy But now I'm not sure what I'm supposed to do. When it said to separate variables, it said that I should put the terms with a y on one side and the terms with a v on the other, but... are there any terms with a y? Other than the dy? I also have no idea how to integrate this equation... Can anybody help me figure out the next few steps? Thank you again. PS: is there a way to actually have it write v(dot) normally - as in, with a dot above the v?