I\'m completely lost, please help! This is a homework problem (notfrom the book)

Question

I'm completely lost, please help! This is a homework problem (notfrom the book)

A spherical raindrop falling through mist builds up mass. The massaccumulates at a rate proportional to its cross-sectional area andvelocity, that is, dm/dt=kr2/v, where r is theradius of the raindrop at any given time and v is the velocity atthe same time. Assume the density of the raindrop isconstant. Ignoring the resistance due to the fog and the air,calculate the instantaneous acceleration of the raindrop as afunction of v,r,,g, and k (Hint-in this variable massproblem, proceed similarly to a rocket problem finding dp/dt andsolving for dv/dt.)

Explanation / Answer

Follow the hint:

        dp/dt = Force

       m dv/dt  +   v dm/dt   =   mg

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