So I think I have found the solution to the following problem, but it feels like I just barely patched it together, if anyone could take a quick peek and make sure I wasn't making up my own math, I would be very appreciative!

So I started with the knowledge that the rate of change of mass is km(t).When a liquid drop falls, it increases in mass. Mass at time is . Rate of growth of the mass of the liquid is for positive constant . When we apply the Laws of Motion, we get , where is the velocity of the liquid drop, and is the acceleration due to gravity. The terminal velocity of the reaindrop is . Find an expression for the terminal velocity in terms of and .

So now I used this result in conjunction with the information : .

Antiderivative of

Now to find the terminal velocity, we take the limit: .

Does this make good sense? Thanks!