How Does Projectile Range Change Over Non-Flat Terrain?

In summary, the speaker is seeking a reliable formula for finding the range of a projectile flying over non-flat ground. They mention that they understand the formula for finding range over flat ground, but are unsure of the validity of a formula they found on Wikipedia. They request an explanation of the Wikipedia formula or the correct formula for non-flat ground, as they need to understand and explain it for an upcoming presentation on ballistics. The speaker also provides the formula for finding range over flat ground, which includes variables for initial velocity, launch angle, gravitational acceleration, and original height of the projectile.
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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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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.
 

1. What is the ballistics range formula?

The ballistics range formula is a mathematical equation used to calculate the maximum distance a projectile will travel when launched at a specific angle and velocity, taking into account the effects of gravity and air resistance.

2. How is the ballistics range formula derived?

The ballistics range formula is derived from the projectile motion equations, which describe the motion of an object under the influence of gravity. By combining these equations with the effects of air resistance, the ballistics range formula is obtained.

3. What factors are included in the ballistics range formula?

The ballistics range formula takes into account the initial velocity of the projectile, the launch angle, the effects of gravity, and the effects of air resistance. It assumes a level and uniform terrain.

4. Can the ballistics range formula be used for any type of projectile?

The ballistics range formula is applicable to any type of projectile, as long as the initial conditions and external factors are known. However, it may not be accurate for objects with irregular shapes or those affected by strong winds.

5. What are some limitations of the ballistics range formula?

The ballistics range formula does not take into account factors such as the rotation of the Earth or the curvature of the Earth's surface, which may affect the accuracy of the calculated range. It also assumes a stationary target and does not consider the effects of wind on the projectile's trajectory.

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