Relationship between horizontal range and angle of launch

[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?

 

[anuttarasammyak]

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.

 

[ayans2495]

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?

 

[anuttarasammyak]

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

 

[ayans2495]

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

Ok, great. Thank you for your reply. I truly appreciate it.

 

[anuttarasammyak]

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.

 

[ayans2495]

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.

 

[jbriggs444]

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.