Projectile Motion
By: Sam, Jacob, and Wendell
Outline
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Drag (air resistance)
How does air density affect trajectory
How does wind affect affect trajectory
Model of a cannon in 3 dimensions
(java)
Recap
• Shoot a projectile at a target
• Time step is .01 seconds
• Optimal angle 45°
How drag works
• Drag = cd * r * V2/2 * A
• Drag coefficient (cd) is a constant on
earth
• Density of the air ( r ) changes with
altitude
• Velocity of the cannon ball (V2)
starts between 400 and 500 m/s
• Surface area of the cannon ball (A) is
0.04524 m2
3D plot
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Added Z axis
Used two graphs to get 3D
Wind in two directions
New angle (Z)
Y,X
X,Z
Density change
Higher altitude less density
No change in density
Wind
• No wind on the Y axis
• Wind factors into drag
No wind
• + wind increases drag • no wind gives the
• - pushes the ball
ball a natural path
a graph with no wind
Results
• Wind has little effect on trajectory of a
cannon ball
• Density change can make a cannon ball go
farther
• Adding the Z axis made it much harder to
hit the target
References
• http://www.grc.nasa.gov/WWW/K12/airplane/falling.html
• http://www.nps.gov/fomc/archeology/canno
n.jpg
• http://orgs.unt.edu/talons/rush/cannon.jpg