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## Main Question or Discussion Point

This past weekend, for fun, I made a pneumatic air cannon, using compressed air to shoot out a small projectile at very high velocity. I'd post my video, but I have not made 15 posts on this forum.

What I need to do is find as close as I can to the actual initial

velocity of a projectile, once it leaves the barrel. If I have the air

cannon pointed at 90 degrees to the ground, than I could shoot the

projectile vertical and time hang time, factoring in known

acceleration of gravity, to find an approx initial velocity. The only

problem is, with a projectile going this fast, with significant

surface area, there will be significant air drag to account for.

As air resistance effects the velocity of the projectile, and as

decreased velocity coincides with a decrease in drag, I believe I will

be needing to use differential equations.

Do you have any idea how I could setup a differential equation to

account for air resistance in my quest to find as close as I can to

the projectile's initial velocity? I have never done anything with air drag before. I just finished Calculus II, but I can put in the nessesary time and effort if someone can get me started here.

Thanks,

John

What I need to do is find as close as I can to the actual initial

velocity of a projectile, once it leaves the barrel. If I have the air

cannon pointed at 90 degrees to the ground, than I could shoot the

projectile vertical and time hang time, factoring in known

acceleration of gravity, to find an approx initial velocity. The only

problem is, with a projectile going this fast, with significant

surface area, there will be significant air drag to account for.

As air resistance effects the velocity of the projectile, and as

decreased velocity coincides with a decrease in drag, I believe I will

be needing to use differential equations.

Do you have any idea how I could setup a differential equation to

account for air resistance in my quest to find as close as I can to

the projectile's initial velocity? I have never done anything with air drag before. I just finished Calculus II, but I can put in the nessesary time and effort if someone can get me started here.

Thanks,

John