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Title:

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
  • Basketball
  • Football
  • Dare Devil Stunts

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

4
Operations
  • Validation
  • Research
  • Compare Models
  • Verification
  • Advanced Calculations
  • 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
(No Transcript)
9
(No Transcript)
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
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