How Does Gravity Affect the Trajectory of an Artillery Shell?

[petitericeball]

Hey, I'm doing a math project on projectiles (I think) and I was wondering how to determine how let's say... an artillery shell would act after it leaves the barrel. I was wondering when the forces of gravity would overcome the initial propulsion force and begin to bring the shell down. I know that the angle of the shot, wind etc. would effect this, but just like a rough estimate.

I'm guessing the flight path would look something like a stretched out parabola, but I'm unsure about how to determine those factors.

 

[kkrizka]

See for more information on projectile motion:
http://id.mind.net/~zona/mstm/physics/mechanics/curvedMotion/projectileMotion/generalSolution/generalSolution.html

 

[astrokreng]

Hello,

Thank you for reaching out regarding your math project on projectiles. I can provide some insights on how to determine the trajectory of an artillery shell.

Firstly, it is important to understand that the motion of a projectile is influenced by both its initial velocity and the forces acting upon it, such as gravity and air resistance. The initial velocity of the shell can be calculated using the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration (in this case, due to the force of the explosion), and t is the time.

To determine when the forces of gravity will overcome the initial propulsion force, you can use the formula s = ut + (1/2)at^2, where s is the distance traveled, u is the initial velocity, a is the acceleration (in this case, due to gravity), and t is the time. This will give you an estimate of the distance the shell will travel before gravity begins to significantly affect its trajectory.

The angle of the shot and wind can also affect the trajectory of the shell. To account for these factors, you can use mathematical models such as the parametric equations for projectile motion, which take into consideration the initial velocity, angle of the shot, and any external forces acting on the projectile.

In terms of the flight path, as you mentioned, it will indeed follow a parabolic path. The exact shape of the path will depend on the initial velocity, angle of the shot, and external forces.

I hope this helps guide you in your project. It is important to note that these calculations are simplified and do not take into account factors such as air resistance and the rotation of the Earth, which can also affect the trajectory of a projectile. For a more accurate estimation, you may need to use more complex mathematical models or perform experiments. Good luck with your project!