4. Falling Drop A raindrop of mass \(m_{0}\), starting from rest, falls under the influence of gravity. Assume that as the raindrop travels through the clouds, it gains mass at a rate proportional to the momentum of the raindrop, \(\frac{d m_{r}}{d t}=k m_{r} v_{r}\), where \(m_{r}\) is the instantaneous mass of the raindrop, \(v_{r}\) is the instantaneous velocity of the raindrop, and \(k\) is a constant with unit \(\left[m^{-1}\right] .\) You may neglect air resistance.(a) Derive a differential equation for the...