Please provide assistance constructing a model which can be used to describe a rain drop:
Question: Lets assume that a very, very small drop of rain starts its way somewhere up in the sky with a mass of m0 and a velocity of 0. We know that when it hits the ground, its usually not that small, and the question of how it grows in mass arises. Its natural to assume that it absorbs other small drops along the way down. The bigger the surface of the drop, the more it can absorb other drops. Therefore we will assume that the rate of change of the mass is proportional to its surface: dm/dt = G*4*Pi*R^2
A. Lets assume that the density P in the drop is constant. What is the mass of the drop as a function of R?
B. Use the previous clause to find a differential equation of the mass of the drop, and solve it, (including initial conditions for the constant) to find m(t).
C. If the velocity of the drop is a function of time, v(t), then what is the momentum of the drop as a function of time, p(t)?
D. Using newton laws, arrive at a function for v(t) and solve it to find the velocity of the drop as a function of time.
The solution analyzes the motion of a falling raindrop.