How Does Projectile Range Change Over Non-Flat Terrain?

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SUMMARY

The discussion focuses on the calculation of projectile range over non-flat terrain, specifically addressing the formula provided by Wikipedia. The formula discussed is r = (VcosA/g)*(VsinA + sqrt((VsinA)² + 2gy), where V represents initial velocity, A is the launch angle, g is gravitational acceleration, and y is the original height. The user seeks clarification on this formula to effectively present the concept of ballistics to classmates.

PREREQUISITES
  • Understanding of basic projectile motion principles
  • Familiarity with the formula for range on flat ground: (v²/g) * sin(2A)
  • Knowledge of gravitational acceleration (g) and its value on Earth
  • Ability to manipulate algebraic equations and square roots
NEXT STEPS
  • Research the derivation of the projectile range formula for non-flat terrain
  • Study the effects of initial height on projectile motion
  • Explore advanced topics in ballistics, including air resistance and its impact on range
  • Learn about numerical methods for simulating projectile motion over varying terrains
USEFUL FOR

Students studying physics, educators teaching projectile motion, and anyone interested in the complexities of ballistics and projectile trajectories over non-flat surfaces.

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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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