9464

Projectile with Air Drag

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.
A significant decrease in the maximum horizontal range is observed when the drag force becomes large. When this value is large, the terminal velocity (the maximum velocity for a falling object) is reduced. Independent of the initial value of the angle, the projectile ends up falling vertically if it stays in the air long enough before it hits the ground.
A more accurate model of air drag considers another contribution proportional to the square of the velocity, but is more difficult to treat analytically.

THINGS TO TRY

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

The equations of motion for the and directions are given by
( increases upward)
where 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
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+