How Does Projectile Range Change Over Non-Flat Terrain?

AI Thread Summary
The discussion centers on the challenge of calculating the range of a projectile over non-flat terrain, contrasting it with the established formula for flat ground. The user seeks clarification on a formula found on Wikipedia, which includes variables for initial velocity, launch angle, gravitational acceleration, and original height. The formula presented is r = (VcosA/g)*(VsinA + sqrt((VsinA)² + 2gy), but the user expresses confusion about its validity and application. Understanding this formula is crucial for the user's upcoming talk on ballistics. Clarification and explanation of the formula's components and their significance are requested for better comprehension.
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Homework Statement


I completely understand the mathematics behind finding the range of a projectile flying over flat ground. But I cannot find a reliable formula for the projectiles range if it is flying over non-flat ground. Wikipedia had a formula but I did not understand how it could be correct. If someone could either explain the wikipedia formula or tell me the real formula and explain why it works, that would be great as I am giving a talk to some classmates on ballistics soon and must be able to understand and explain the formula.


Homework Equations


When finding the range of a projectile flying over flat ground, the formula for (v2/g)*sin2A
where g is gravitational acceleration on Earth and A is the angle at which the projectile is fired.


The Attempt at a Solution



wikipedia formula?
r= (VcosA/g)*(VsinA+sqrroot((VsinA)2+2gy))

V=initial velocity
A=angle at which projectile was launched
g=gravitational acceleration on earth
y=original height of projectile

Thanks!
 
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