Projectile Motion: Initial Velocity Derivation

[PhysicsIBStudent]

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.

 

[berkeman]

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

 

[PhysicsIBStudent]

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

 

[Tom.G]

Equation (12) is suspicious. According to (12) what is the range when the projectile is launched horizontally (θ = 0)?

 

[PhysicsIBStudent]

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.