Air Cannon Projectile Velocity Calculations help please

[grapefruit355]

Hi everyone, I am new here at Physics Forums and this is my first post.

Earlier this evening, my dad and I were trying to figure out the initial velocity of our projectiles. We were successful in calculating the initial velocity in a vacuum, but we are perplexed as to how to calculate the velocity in air. Here is the data we gathered:

Total distance traveled by projectile: 380ft
Time to impact from launch: 2.5 seconds
Angle of launch: 45 degrees
Temperature at time of launch: 45 degrees Fahrenheit
Dimensions of projectile: 2 inch diameter x 3 inch long cylinder
Force of gravity: 32.15223 ft/s/s

Initial Velocity in a vacuum: ~111 feet-per-second

Again, we would like to know the initial velocity of the object traveling through the air. If you can provide an answer, that's great, but we would also like an explanation to feed our starving minds :)

Cheers, and thanks in advance!

 

[K^2]

You need to also provide mass of the projectile.

There is no analytical solution to a projectile with drag, because horizontal and vertical motions don't separate. Pure vertical motion has a solution, however. If there is a way to safely fire the thing straight up and time the flight, that data can yield initial velocity. Especially if you run a separate experiment to find terminal velocity of your projectile.

Initial velocity neglecting drag results in too large a disparity with your time of flight. It should be closer to 5s. Even if your projectile tumbled, I don't see how drag alone would account for that big a difference. Wind wouldn't account for that either, though, that's another thing you might want to mention.