# Relationship between horizontal range and angle of launch

• ayans2495
In summary: Air resistance will definitely add to the drag and cause the projectile to deviate from a perfect parabola.
ayans2495
Homework Statement
How does the angle at which a projectile is launched vary with respect to the horizontal range it covers?
Relevant Equations
R = u^2(sin(2(theta))/g,
I would like to conduct an experiment asking the question "how does the angle at which a projectile is launched vary with respect to the horizontal range it covers?" Ultimately, I'd like to prove that the horizontal range is directly proportional to sin(2(theta)). This will be done with the aid of a cannon. However, how do I ensure that the initial velocity is constant? As I change the angle, do I change the projectile's initial velocity? Namely, how do I control the horizontal initial velocity to yield this linear relationship?

Last edited:
ayans2495 said:
This will be done with the aid of a cannon. However, how do I ensure that the initial velocity is constant?

With same amount of gun powder you may eject bullets with constant velocity for various launch angles.

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Steve4Physics
anuttarasammyak said:
With same amount of gun powder you may eject bullets with constant velocity for various launch angles.
What if it's launched by a spring? Would I have to adjust the tension accordingly or maintain the same applied forces?

Spring or rubber for catapult should be contracted / stretched to the same length for any launch angles.

anuttarasammyak said:
Spring or rubber for catapult should be stretched to the same length for any launch angles.

We should take care that the initial position of the bullet at rest should be at same height or ground so that the elastic energy should not be converted to potential energy during the launching process.

anuttarasammyak said:
We should take care that the initial position of the bullet at rest should be at same height or ground so that the energy should not be consumed / added for the change of potential energy during the launching process.
Yes, I understand why that is. So the height from which the projectile is launched ought to be controlled.

Exterior ballistics in the presence of air resistance is difficult. If you scroll down to the graphs in this article, you will see that actual trajectories are not parabolic. That should give you some qualms about assuming adherence to a model in which air resistance is zero.

gmax137

## What is the relationship between horizontal range and angle of launch?

The horizontal range and angle of launch have a direct relationship, meaning that as the angle of launch increases, the horizontal range also increases. This is because a higher angle of launch results in a longer flight path for an object, leading to a greater horizontal distance covered.

## How does the angle of launch affect the horizontal range?

The angle of launch has a significant impact on the horizontal range of an object. A lower angle of launch results in a shorter flight path and therefore a shorter horizontal range, while a higher angle of launch leads to a longer flight path and a greater horizontal range.

## What is the optimal angle of launch for maximizing horizontal range?

The optimal angle of launch for maximizing horizontal range depends on several factors, such as the initial velocity and air resistance. However, in most cases, it is found that a launch angle of around 45 degrees provides the maximum horizontal range.

## How does air resistance affect the relationship between horizontal range and angle of launch?

Air resistance can significantly impact the relationship between horizontal range and angle of launch. As air resistance increases, the horizontal range decreases, meaning that the angle of launch must be adjusted to achieve the desired horizontal range.

## Is there a limit to how far an object can travel horizontally based on the angle of launch?

Yes, there is a limit to how far an object can travel horizontally based on the angle of launch. This is because as the angle of launch increases, the vertical component of the initial velocity also increases, resulting in a shorter flight time and therefore a shorter horizontal range.

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