(adsbygoogle = window.adsbygoogle || []).push({}); 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 = kvm^{2/3},

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 = kvm^{2/3}".

I am unsure where to begin, any help in pointing me in the right direction would be greatly appreciated.

Thank you.

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# The change of mass with respect to time of a rain drop falling though a cloud

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