A rain drop of initial mass m0 starts falling from rest under the influence of gravity. Assume that the drop gains mass from the cloud at a rate proportional to the product of its instantaneous mass and its instantaneous velocity: dm = km v , where k is a constant. Show that the speed of the drop eventually becomes dt effectively constant, and give an expression for the terminal speed. Neglect air resistance.
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A raindrop with initial mass M0 starts falling from rest under the influence of gravity. Assume that the drop gains mass from the cloud at a rate proportional to the product of its instantaneous mass and velocity:
dM/dt = k M v where k is a constant. Show that the speed of the drop approaches a constant after a long time, derive an expression for the terminal speed, and calculate the terminal speed. Neglect air resistance.
Data: M0 = 0.6 grams; k = 0.06 m^-1
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