- #1

Astrum

- 269

- 5

## Homework Statement

First time I've had to deal with ODEs, an I'm pretty confused.

This SHOULD be a simple ODE for finding air resistance, that is only dealing with the y vector (up and down in this case)

[itex]m\frac{dv_{y}}{dt}=mg-kv_{y}[/itex]

## Homework Equations

F=ma

f=-kV

## The Attempt at a Solution

First order differential equation, so we only need to integrate once.

[tex]m\frac{dv_{y}}{dt}=mg-kv_{y}=g-\frac{kv}{m}[/tex]

[tex]\int\frac{dv}{dt}=gt-\frac{k}{m}\int v dt[/tex]

I have no idea where to go from here. The answer in the book gives:

[tex]v=\frac{mg}{k}(1-e^{-\frac{kt}{m}})[/tex]