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Momentum raindrop: Show that speed eventually becomes effectively constant; give expression for terminal speed

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A raindrop of initial mass Mo starts falling from rest under the influence of gravity. Assume that the drop gain mass from the cloud at a rate proportionnal to the product of its instantaneous mass and its instantaneous velocity:
dM/dt = kMV where k is a constant.

Show that the speed of the drop eventually becomes effectively constant, and give an expression for the terminal speed. Neglect air resistance

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