Need help with projectile motion problem

[kwaber1]

I found this interesting problem on the internet, but I think there is not enough infromation to solve.
"At the 1998 Punkin Chunkin World Championship, a pneumatically-driven device called the "Aludium Q36 Pumpkin Modulator" was able to project a 3.6-4.5 kg (8-10 pound) pumpkin intact for a total distance of 1227.23 m (4026.32 feet, how many feet are in a mile?). What was the muzzle velocity (magnitude and direction) of the record-setting pumpkin?"

Most range formula problems give you 2 of the 3 variables to solve for the third R, v_o or Θ
Any help would be appreciated.

 

[Herman Trivilino]

Neglecting the effects of friction (a necessary but absurd assumption) there is a value of $\theta$ that gives you the maximum range. I think it's understood that the pumpkin was chucked at this angle.

 

[JRMichler]

The optimal angle for maximum range in a vacuum is 45 degrees. When the effect of air resistance is included, it's between 30 and 45 degrees.

The definitive book on the subject is Modern Practical Ballistics, by Arthur J. Pejsa. The equations in that book may not cover objects with the (low) ballistic coefficient of pumpkins. If so, numerical methods are needed.

For a shotgun with birdshot fired at (very roughly) 30 degree elevation, the pellets come almost straight down at maximum range. This from a test where my dad had my mother shoot at him. Unfortunately, she had no experience with a double barrel shotgun with double triggers, so she fired both barrels at the same time and got knocked down from the recoil. That ended further testing.

 

[Dr.D]

For a shotgun with birdshot fired at (very roughly) 30 degree elevation, the pellets come almost straight down at maximum range. This from a test where my dad had my mother shoot at him. Unfortunately, she had no experience with a double barrel shotgun with double triggers, so she fired both barrels at the same time and got knocked down from the recoil. That ended further testing.

This is a fascinating report. One could speculate all day about your parents relationship (lol!). Considering the legal/moral/ethical aspects of this situation, it is probably best that testing ended at that point.