# Trajectories - PowerPoint PPT Presentation

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## Trajectories

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### Euler's Method: New = Old Change. Vy new = Vy old g ?t. Vx new = Vx old ... http://id.mind.net/~zona/mstm/physics/mechanics/curvedMotion/projectileMoti on ... – PowerPoint PPT presentation

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Title: Trajectories

1
Trajectories
• By
• Zack Stutts
• Freddy Sonnenwald

2
Uses
• ? Cold War
• Ballistic Missile
• Nuclear
• Biological
• Conventional
• Napoleonic War
• Cannon
• Sports/Entertainments
• Football
• Dare Devil Stunts

3
The Question
• Velocity
• Angle
• Time steps
• Gravity

4
Operations
• Validation
• Research
• Compare Models
• Verification
• Eulers Method
• An Excel Workbook
• A Java Program

5
Architecture
• Microsoft Excel
• Sun Java

6
Estimating Math
• Eulers Method New Old Change
• Vy new Vy old g ?t
• Vx new Vx old ø
• X new X old Vx ?t
• Y new Y old Vy ?t

7
Exact Math
• Exact Mathematical Equation
• Y at t Y init Vy init t (1/2 g t²)
• X at t X init Vx init t

8
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9
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10
Excel Estimated
• Eulers Method
• Difference lt 15 m
• Reasonable Distance
• Fits on Graph

11
Excel Exact
• Exact Calculations
• Reasonable Distance
• Fits on Graph

12
Java
• Both exact/estimated
• Finds height/distance

13
Results
• Eulers Method Perfect
• Time steps dependant
• Velocity effective
• 45 degrees high range
• Gravity Important

14
Sources
• http//www.physicsclassroom.com/Class/vectors/U3L2
e.html the formulas
• http//www.civilwarartillery.com/projectiles/spher
ical/IIIA3.htm velocity of a cannonball
• http//id.mind.net/zona/mstm/physics/mechanics/cu
rvedMotion/projectileMotion/generalSolution/genera
lSolution.html general information