# Angle required to hit coordinates x, y, z with air ressitance

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• TheShermanTanker
In summary, the formula for the angle required to launch a projectile with given velocity, gravity, distance, and height difference is tan-1((v^2 +/- square-root(v^4 - g(gx^2 + 2yv^2)))/gx). However, this formula assumes that the only resistive force is gravity and that there is no horizontal resistance present. To factor in air resistance, integration of the equations of motion is needed. The drag model being used may work for short flight times, but may not be as accurate for longer flight times.
TheShermanTanker
The formula for the angle required for you to launch a projectile with a given velocity, gravity, distance and height difference is, taking g as gravity, v as total velocity, x as total distance on the horizontal plane and y as how high the target is above you (Negative value means the target is below you) is
tan-1((v^2 +/- square-root(v^4 - g(gx^2 + 2yv^2)))/gx). However, this assumes that the only resistive force is on the vertical plane (gravity) and that there is no horizontal resistance present (air resistance). However, the thing that I'm working on now has a hard-coded air resistance value of 1% of the object's current velocity that takes effect every 1/20 of a second (Basically imagine taking the object's velocity and multiplying it by 99% every twentieth of a second). Is there a way to factor air resistance in as well?

No analytic expression, I am afraid. So you have your numerical work (in the other thread) cut out for you

By the way, better not to call gravity force 'resisitive': it is a so-called conservative force: the work it does is converted into kinetic energy. For resisitive forces the work goes into heat and/or deformation.

TheShermanTanker
TheShermanTanker said:
Is there a way to factor air resistance in as well?

I'll also page @Dr. Courtney to see if he has better links or thoughts.

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TheShermanTanker
No closed for solution. As mentioned above, the needed approach is to integrate the equations of motion.

But the drag model you are working with seems unusual and slightly contrived. It might work ok for relatively short flight times.

TheShermanTanker

## 1. What is the equation for calculating the angle required to hit a specific coordinate with air resistance?

The equation for calculating the angle required to hit a specific coordinate with air resistance is:
θ = arctan((v2 ± √(v4 - g(gx2 + 2yv2)))/(gx))
where θ is the angle, v is the initial velocity, g is the acceleration due to gravity, x is the horizontal distance, and y is the vertical distance.

## 2. How does air resistance affect the angle required to hit a specific coordinate?

Air resistance affects the angle required to hit a specific coordinate by decreasing the horizontal distance and increasing the vertical distance. This means that a higher angle is required to reach the same coordinates compared to a scenario with no air resistance.

## 3. Can the angle required to hit a specific coordinate be calculated without considering air resistance?

Yes, the angle required to hit a specific coordinate can be calculated without considering air resistance using the equation:
θ = arctan(y/x)
where θ is the angle, x is the horizontal distance, and y is the vertical distance. However, this equation assumes no air resistance and may not accurately predict the angle needed in real-world scenarios.

## 4. How does the initial velocity affect the angle required to hit a specific coordinate with air resistance?

The initial velocity has a significant impact on the angle required to hit a specific coordinate with air resistance. A higher initial velocity will result in a lower angle needed to reach the same coordinates, as the projectile will travel further horizontally before being affected by air resistance.

## 5. Are there any other factors besides air resistance and initial velocity that affect the angle required to hit a specific coordinate?

Yes, there are other factors that can affect the angle required to hit a specific coordinate, such as the shape and weight of the projectile, wind speed and direction, and the surface area and density of the medium the projectile is traveling through. These factors can all impact the amount of air resistance experienced by the projectile and therefore affect the angle needed to reach a specific coordinate.

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