# Falling Meteor

A meteor of initial mass $$m_{0}$$ enters the earths atmosphere and starts falling from rest under the influence of gravity. Assume that the meteor gains mass from the cloud at a rate proportional to the momentum of the meteor, $$\frac { d{ m }_{ 0 } }{ dt } =k{ m }_{ 0 }v$$ , where $$v$$ instantaneous velocity of the meteor. If $$k$$ is equal to $$5 m^{-1}$$, what will be the terminal velocity of the meteor?

Take into consideration the buoyant force of the cloud

Details and assumption

You may neglect air resistance.

Take gravitational acceleration $$9.8m/{ s }^{ 2 }$$

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