If a raindrop is small - say the diameter of around 0.003in, such as might be fo

Question

If a raindrop is small - say the diameter of around 0.003in, such as might be found in drizzle - it' known from fluid dynamics experiments that the air resistance it encounters is proportional to its speed. The velocity of the raindrop falling from rest is then described by the initial value problem

(a)Solve the initial value problem by hand

(c) Describe the behavior of your solution

(d) Calculate the terminal velocity of the raindrop (the velocity that it will approach after it has falleb for a long time). Assuming the raindrop reaches (essentially) terminal velocity before it hits the ground, how fast will it be going in miles per hour when it hits?

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