Falling Meteor

A meteor of initial mass m0m_{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, dm0dt=km0v\frac { d{ m }_{ 0 } }{ dt } =k{ m }_{ 0 }v , where vv instantaneous velocity of the meteor. If kk is equal to 5m15 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/s29.8m/{ s }^{ 2 }

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