= Accreting raindrop with quadratic drag
{title2=$\dot a=cv/4,\quad\dot v=g-3(c+k)v^2/(4a)$}
For a spherical drop of constant <mass density> $\rho$, radius $a>0$ and downward <velocity> $v>0$, suppose its volume grows at rate $c\pi a^2v$ by collecting stationary mist and its upward <quadratic drag> is $k\rho\pi a^2v^2$, with $c,k>0$. The drop <mass> is $4\pi\rho a^3/3$. Its incoming <mass accretion rate> and the <variable-mass system> momentum law give the displayed equations. The accreted matter must be accelerated from rest, producing the additional $c$ term alongside drag.
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