Falling Meteor

Classical Mechanics Level 4

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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