1. The problem statement, all variables and given/known data A 20 kg rock falls with the force of gravity acting on it. Another force acts on the rock (same direction as gravity) that is proportional to the velocity squared, 100v^2. Come up with an expression of the rock's velocity at any time t. 2. Relevant equations Hint: (d/dx)(tan^-1(x)) = 1/(1 + x^2) 3. The attempt at a solution F(net) = ma = Fg + 100v^2 ma = mg + 100v^2 a = g +(100v^2)/m (m=20) dv/dt = g + 5v^2 dv/dt = g((5/g)v^2 + 1) dv/((5/g)v^2 + 1) = g(dt) dv/((root(5/g)*v)^2 +1) = g(dt) (integrate both sides) tan^-1(root(5/g)*v) = gt + C root(5/g)*v = tan(gt + C) v(t) = (root(g/5))tan(gt + C) I want to know if I can get rid of the constant as well as if my approach to the general solution is correct. Also if my general soln is correct. Thanks!