An Object with Mass $m$ Is Dropped from Rest and We Assume That the Air

question 44

Short Answer

An object with mass $m$ is dropped from rest and we assume that the air resistance is proportional to the speed of the object. If $s ( t )$ is the distance dropped after $t$ seconds, then the speed is $v = s ^ { \prime } ( t )$ and the acceleration is $a = v ^ { \prime } ( t )$ . If $g$ is the acceleration due to gravity, then the downward force on the object is $m g - c v$ , where $c$ is a positive constant, and Newton's Second Law gives $m \frac { d v } { d t } = m g - c v$ . Find the limiting velocity.

---

Definitions:

Keyboard

An input device comprised of a set of keys, including alphabetic, numeric, and functional keys, used for typing text, entering commands, and controlling functions on a computer or device.

Trackball

A pointing device consisting of a ball housed in a socket containing sensors to detect rotation.

Clipboard

A temporary storage area in operating systems and applications for data that the user wishes to copy from one place to another.

Copy

The action of duplicating data or files from one location to another; commonly used in computer operations to create a duplicate instance of a file.