1. The problem statement, all variables and given/known data Good day all! I'm stumped on a question: If I fire a bullet straight up what will be the initial velocity such that the bullet doesn't come back down? I need to model a differential equation (it will be first order) some how! Also, Gravity is not constant, but rather, the acceleration due to gravity dv/dt is -k/r^2 where k is a positive constant and r is the distance to the center of the earth (4000 mi) 2. Relevant equations Also, dv/dt=(dv/dr)v 3. The attempt at a solution My teacher said something about at the point where the initial velocity is great enough to over come gravity, the root in the de will become complex. That's all I know. Any help would be appreciated! So far I know: m(dv/dt)=-mg and g=-k/r^2 I can find a de for v(r) easily since the eqn is seperable, but I'm not sure what to do with it.... Also, the problem gives g at the surface of earth as -32 ft/s^2, and r in miles, so unfortunately we aren't using metric here. Thanks!!!