1. The problem statement, all variables and given/known data A raindrop is falling through a cloud, collecting water as it falls. If the raindrop has mass m and velocity v, show that mg = vdm/dt +mdv/dt. Assume that the drop remains spherical and that the rate of accretion is proportional to the cross-sectional area of the drop multiplied by the speed of fall. Show that this implies that dm/dt = kvm2/3, for some constant k. Using this equation and the assumption that the drop starts from rest when it is infinitesimally small, find m as a function of x. Hence show that the acceleration of the raindrop is constant and equal to g/7. I have managed to show that mg = vdm/dt +mdv/dt easily, but I am at a lose for the second part where the question asks "Show that this implies that dm/dt = kvm2/3". I am unsure where to begin, any help in pointing me in the right direction would be greatly appreciated. Thank you.