Projectile Motion: Initial Velocity Derivation

AI Thread Summary
The discussion revolves around the challenges of deriving an accurate mathematical model for projectile motion, specifically for a water rocket experiment. The user is comparing theoretical results with experimental data but finds significant discrepancies, particularly in initial velocity calculations. They acknowledge the omission of drag in their model and seek feedback on its accuracy. Concerns are raised about a specific equation in their model, which appears problematic when considering horizontal launches. The conversation highlights the importance of ensuring assumptions in the model align with the experimental conditions.
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Hey guys, I am working on a school project and have fired some water rockets at different angles. I am now trying to compare theoretical results vs experimental results. But I am struggling to produce an accurate mathematical model.

I have attached my attempt to this post. It is quite long and possibly overly complex. I have not taken drag into account for this model.

I have compared the range results I got from my model to some from a water rocket simulator which was fed the same initial conditions but they are very different.

My question is whether my model is anywhere close to correct or where I went wrong. I used data from my water rocket to attempt to find the initial velocity of the rocket. I don't think my initial speed is correct tho.
 

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Can you upload a PDF version of the file please? DOCX file format is not as secure as PDF format. Thanks.
 
berkeman said:
Can you upload a PDF version of the file please? DOCX file format is not as secure as PDF format. Thanks.

Done. Please let me know if there are issues opening the pdf
 
Equation (12) is suspicious. According to (12) what is the range when the projectile is launched horizontally (θ = 0)?
 
Tom.G said:
Equation (12) is suspicious. According to (12) what is the range when the projectile is launched horizontally (θ = 0)?

Your right I forgot to mention this equation assumes you are launching from ground-level and the ground is flat. The formula only intends to work for non zero angles as launching at 0 degrees would result in a crash of some sort.
 
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