Projectile Motion, not as easy as you think., need help?

Question

I have a non-uniform wind vector acting on my projectile. The wind vector changes as a function of x ,y ,and z. I would like to be able to solve for the angle above the horizon the gun should be pointed, and the angle off of the x-axis (in the x,y plane) the gun should be pointed in order to hit a target a certain distance above the horizon. If my initial position vector is [0 , 0 , 0] and my final targets position is [300 , 0 , 15]. Any thoughts would be awesome. I am solving this using MatLab, and have a program that will tell me every position of the ball during it's flight.

Answer 1

You need a differential equation solver and I'm sure there are multiple types built-in to Matlab. If you Google differential equation + projectile, I'm sure you'll find all the help you need.

The 'basic' concept is that at each time step, you compute where the projectile is compared to where it needs to be and back-apply a correction to the initial conditions.


EDIT.....

I should have been more specific. You have a boundary value problem, not an initial value problem.

check this out
http://amath.colorado.edu/courses/3050/2007Spr/Projects/Shooting/shooting.pdf

Answer 2

♠ yes, I’ve got an idea and I’m aware it must be a hard problem. If you have that mysterious MatLab hand and a program that will tell you every position of the ball during its flight what the hεκκ I’m supposed to do then? Click me though if you really need any help. and explain the situation.

Answer 3

That DOES sound harder than I thought. Without knowing the wind function I would have a hard time giving an answer, but basically I think you just need to add the acceleration of gravity to the vertical component (would that be Y or Z?) of your wind function and then solve it. That could be reasonably easy or extremely difficult, depending on the exact wind function.