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Trajectories

Trajectories. By: Zack Stutts Freddy Sonnenwald. Uses.  Cold War Ballistic Missile Nuclear Biological Conventional Napoleonic War Cannon Sports/Entertainments Basketball Football Dare Devil Stunts. The Question. Velocity Angle Time steps Gravity. Operations. Validation

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Trajectories

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  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 • Euler’s Method • An Excel Workbook • A Java Program

  5. Architecture • Microsoft Excel • Sun Java

  6. Estimating Math • Euler’s Method: New = Old + Change • Vy new = Vy old + g ·Δt • Vx new = Vx old + ø • X new = X old + Vx ·Δt • Y new = Y old + Vy ·Δt

  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. Excel Estimated • Euler’s Method • Difference < 15 m • Reasonable Distance • Fit’s on Graph

  9. Excel Exact • Exact Calculations • Reasonable Distance • Fits on Graph

  10. Java • Both exact/estimated • Finds height/distance

  11. Results • Euler’s Method Perfect • Time steps dependant • Velocity effective • 45 degrees high range • Gravity Important

  12. Sources • http://www.physicsclassroom.com/Class/vectors/U3L2e.html the formulas • http://www.civilwarartillery.com/projectiles/spherical/IIIA3.htm velocity of a cannonball • http://id.mind.net/~zona/mstm/physics/mechanics/curvedMotion/projectileMotion/generalSolution/generalSolution.html general information

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