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# When a raindrop falls, it increase in size and so its mass at time $t$ is a function of $t,$ namely, $m(t).$ The rate of growth of the mass is $km(t)$ for some positive constant $k.$ When we apply Newton's Law of Motion to the raindrop, we get $(mv)' = gm,$ where $v$ is the velocity of the raindrop (directed downward) and $g$ is the acceleration due to gravity. The terminal velocity of the raindrop is lim $_{t \to \infty} v(t).$ Find an expression for the terminal velocity in terms of $g$ and $k.$

## $$\lim _{t \rightarrow \infty} v(t)=g / k$$

#### Topics

Differential Equations

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##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

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### Video Transcript

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#### Topics

Differential Equations

##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp