# Projectile with Air Drag

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

The plots show projectile motion with air resistance (red) compared with the same motion neglecting air resistance (blue). The projectile is launched at an angle with initial velocity *. *The force due to air resistance is assumed to be proportional to the magnitude of the velocity, acting in the opposite direction.

Contributed by: Enrique Zeleny (April 2009)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The equations of motion for the and directions are given by

,

where increases upward and is a positive constant. The terminal velocity is given by , so the equations can be simplified to

.

For a projectile launched at an angle , and .

Integration of the equations of motion gives

,

## Permanent Citation