1. The problem statement, all variables and given/known data A projectile that is subject to quadratic air resistance is thrown vertically up with initial speed v0. (a): Write down the equation of motion for the upward motion and solve it to give v as a function of t. (b): Show that the time to reach th top of the trajectory is ttop = (vter/g)arctan(v0/vter. 2. Relevant equations ma = -cv2 3. The attempt at a solution I think I may have done something wrong with part a which is leading me astray for part b. Part (a): m dv/dt = mg - cv2 vter occurs when mg = cv2 vter = sqrt (mg / c) solving for c, I get: c = (mg / (vter)2) Putting this back in to my differential equation and cancelling the mass out: dv/dt = g(1 - (v2 / vter2)) Integrating both sides, I get: gt = vterarctanh(v/vter) - vterarctanh(v0/vter) solving for v as a function of t, I get: v(t) = vtertanh((gt/vter) + arctanh(v0/vter)) Therefore, for part b, when it is at the top of its flight, v(t) = 0. Substituting in the zero and solving for t, I get: (vter/g)arctanh(v0/vter) As you can see, this is almost what the correct answer is, except it should be a function of the inverse tangent of v0 / vter, NOT the inverse hyperbolictangent. Any ideas where I went wrong or what I am missing here? Thanks in advance.