Determine the law of motion of a freely falling rain

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Determine the law of motion of a freely falling rain drop if air resistance is described by the law F = aV ^ 2, where V is the absolute value of the velocity of the drop at a given time. After what time can the droplet speed be considered constant?

Task 11185. Detailed solution with a brief record of the conditions, formulas and laws used in the decision, the conclusion of the calculation formula and the answer.
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