How Does a Vector Field Affect a Projectile's Path?

[saminator910]

So I was wondering if I defined a vector field F, and a Trajectory of a particle x=t y=.5at^2+vit+si
and I can find the work done by the field on a particle moving on a path with a line integral ∫F.dr, so what would this equate to for a projectile does it apply to this?, could you give me a real life example, could it possibly be wind? but wind would change it's path right? Thank you for any response.

 

[haruspex]

Any field will affect the path. You could consider a particle on a constrained path, like a bead on a wire, but then you need to bring in the force exerted by the wire.