$\"\"$

\

The rate of growth of mass is $\"\"$ , where $\"\"$ is mass as a function of $\"\"$ .

\

Hence , $\"\"$ .

\

Newtons law of motion to the rain drop is $\"\"$ . \ \

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Where $\"\"$ is the velocity of the raindrop and $\"\"$ is the acceleration.

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Find the terminal velocity of the raindrop is $\"\"$ .

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Consider $\"\"$ .

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Rewrite the expression as $\"\"$ .

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Apply product rule of derivative : $\"\"$ .

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Apply integral on each side.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Therefore, the terminal velocity of the raindrop is $\"\"$ .

\

$\"\"$

\

The terminal velocity of the raindrop is $\"\"$ .