How Does Projectile Range Change Over Non-Flat Terrain?

[Unredeemed]

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!

 

[Unredeemed]

anyone?

 

[Moetasim]

As a scientist, it is important to understand the principles and assumptions behind any formula or equation. In the case of the ballistics range formula, it is important to consider the factors that affect the trajectory of a projectile, such as gravity, air resistance, and the shape and size of the projectile itself.

The formula you mentioned for a projectile flying over flat ground assumes that there is no air resistance and that the ground is flat, so the only force acting on the projectile is gravity. This simplifies the calculation and makes it easier to understand the basic principles.

However, when dealing with non-flat ground, the formula becomes more complex because there are additional factors to consider. The wikipedia formula you mentioned takes into account the initial velocity, the angle at which the projectile is launched, the gravitational acceleration, and the original height of the projectile. It also includes the term for air resistance, which can significantly affect the trajectory of a projectile flying over non-flat ground.

The reason why this formula works is because it takes into account the various forces acting on the projectile and their effects on its motion. By including the term for air resistance, it accounts for the fact that the projectile will experience a drag force as it travels through the air, which will decrease its range.

It is important to note that this formula is an approximation and may not be completely accurate in all situations. Factors such as wind speed and direction, atmospheric conditions, and the shape and size of the projectile can all affect its trajectory and ultimately its range.

In summary, the wikipedia formula for ballistics range over non-flat ground is a more comprehensive equation that takes into account the various forces acting on the projectile. It is based on the same principles as the formula for flat ground, but also considers the effects of air resistance and the shape of the terrain. As with any formula, it is important to understand the assumptions and limitations in order to use it effectively.