A spherical raindrop falling through mist builds up mass. The mass accumulates at a rate proportional to its cross-sectional area and inversely proportional to its velocity, that is, dm/dt=kΠr2/v, where r is the radius of the raindrop at a given time and v is the downward speed at the same time. Assume the density ρ of the raindrop is a constant. Ignoring the resistance due to the fog and the air, calculate the instantaneous acceleration of the raindrop as a function of v, r, ρ , g, and k.
(Hint- in this variable mass problem, proceed similarly to a rocket problem in finding dp/dt and solving for dv/dt. Some of the above variables may also cancel out.)