A raindrop of mass mo, starting from rest, falls under the influence of gravity. Assume that...

 

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A raindrop of mass mo, starting from rest, falls under the influence of gravity. Assume that as the raindrop travels through the clouds, it gains mass at a rate proportional to the momentum of the raindrop, dm = km,v,r, where m, is the instantaneous mass of the raindrop, v, is the instantaneous velocity of the raindrop, and k is a constant with unit [m-1]. You may neglect air resistance. (a) Derive a differential equation for the raindrop's accelerations de in terms of k, g. and the raindrop's instantaneous velocity v,. Express your answer using some or all of the following variables: k, g for the gravitational acceleration and v, the raindrop's instantaneous velocity. (b) What is the terminal speed, vr, of the raindrop? Express your answer using some or all of the following variables: k and g for the gravitational acceleration. A raindrop of mass mo, starting from rest, falls under the influence of gravity. Assume that as the raindrop travels through the clouds, it gains mass at a rate proportional to the momentum of the raindrop, dm = km,v,r, where m, is the instantaneous mass of the raindrop, v, is the instantaneous velocity of the raindrop, and k is a constant with unit [m-1]. You may neglect air resistance. (a) Derive a differential equation for the raindrop's accelerations de in terms of k, g. and the raindrop's instantaneous velocity v,. Express your answer using some or all of the following variables: k, g for the gravitational acceleration and v, the raindrop's instantaneous velocity. (b) What is the terminal speed, vr, of the raindrop? Express your answer using some or all of the following variables: k and g for the gravitational acceleration.