trajectories by: zack stutts freddy sonnenwald. uses cold war –ballistic missile nuclear...
TRANSCRIPT
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– Research
• Compare Models
• Verification– Advanced Calculations
• Euler’s Method
• An Excel Workbook• A Java Program
Architecture
• Microsoft Excel
• Sun Java
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
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
Excel Estimated
• Euler’s Method– Difference < 15 m
• Reasonable Distance– Fit’s on Graph
Dropping Estimated
0
2000
4000
6000
8000
10000
0 5000 10000 15000 20000 25000
X- Distance Estimated
Excel Exact
• Exact Calculations• Reasonable Distance
– Fits on GraphDropping Exact
0
2000
4000
6000
8000
10000
0 5000 10000 15000 20000 25000
X- Distance Exact
Java
• Both exact/estimated• Finds height/distance
Results
• Euler’s Method Perfect
• Time steps dependant
• Velocity effective
• 45 degrees high range
• Gravity Important
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