Trajectories

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Trajectories

• By
• Zack Stutts
• Freddy Sonnenwald

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Uses

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

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The Question

• Velocity
• Angle
• Time steps
• Gravity

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Operations

• Validation
• Research
• Compare Models
• Verification
• Advanced Calculations
• Eulers Method
• An Excel Workbook
• A Java Program

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Architecture

• Microsoft Excel
• Sun Java

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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

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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

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Excel Estimated

• Eulers Method
• Difference lt 15 m
• Reasonable Distance
• Fits on Graph

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Excel Exact

• Exact Calculations
• Reasonable Distance
• Fits on Graph

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Java

• Both exact/estimated
• Finds height/distance

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Results

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

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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