Projectile Motion 2.0- Drag in RL

[ultrapowerpie]

So I'm writing a Scientific Lab Inquiry (college research lab write up), and my professor pointed out a major error in my assumption of air/mathematics but I can't for the life of me figure out what is wrong or how to fix it.

Attached is a copy of the paper in all it's glory/infamy. There's a few comments on there, the major one I want to focus on is where he points out that the acceleration for the air resistance
is incorrect. That is the primary part we're focusing on since that alone throws off all calculations/assumptions for the rest of the paper, but if you have any other feedback it'd be appreciated since I'm not used to this type of writing.

But to sum it up: I need help determining the equations of projectile motion with air resistance calculated in. I WAS using a discrete method since I'm using Excel and I can just plug in the formula from the data and just have it generate everything, rather then try using a continuous method which I assume would involve programming

Thanks in advance for your help on the matter!

 

[ultrapowerpie]

Want to say thanks to the mentors for moving this to the correct forum and for anyone who can help.

As an added note, I think the major point of confusion here is that I messed up the assumption on air resistance but I don't know how to fix it or how the original assumption is wrong.

Thank you again for your help :D

Oh, and yes, everything is in the PDF file. But it's only the first few pages that are currently rel event to the situation.

 

[haruspex]

At the first point marked 'not right' you seem to have taken acceleration due to drag to be constant. If we go back to what you had previously, F_x = -D*v*v_x, that leads to the differential equation md²x/dt² = -D((dx/dt)²+(dy/dt)²)^1/2dx/dt

 

[ultrapowerpie]

ack, I thought i had accounted for that. Yeah that would be a huge mix up since air resistance is not constant.

Ah, I see, thank you. Then from THAT acceleration equation I can build up a new velocity and new displacement equation that includes a non-constant acceleration, which should fix many of the discrepancies I found in the data when I plugged it into Excel. That in turn should fix a good chunk of the paper. Thank you very much!