Uncovering the Best Angle for Projectile Motion: 30º vs. 45º Explained

[reinaldo]

Projectile motion!

Hey!...in college they teach you that the most efficient angle for projectile motion is the 45º, cause it gives you the farther distance...but when we did the experiment in the lab we obtain that the best angle (the most distance achived by the metal ball)...was 30º...the teacher said that it was not wrong...in fact...she said...you are shooting it at 30º and you`re getting more distance than with 45º...she asked us to explain why that could happend...

anyways...that happen 2 years ago...i did pass my 1st semester of Physics because with all the other exams and lab test...but she never wanted to explain why that happend!...she said that we should investigate ourselves...i have never got to know why...the only thing i could come up was that since i live in venezuela so I am technically in the middle of the world, it might have something to do with gravity or something like that...

so please...can anyone tell me why did that happened!...thanks!

 

[Dieseltwitch]

two words... air resistance

A projectile travailing at 45 deg will lose more velocity over less ground covered then a projectile at 30 deg

 

[reinaldo]

Air Resistance??...but every Physics Book says that is the 45° angle that has the more distance shooting...Serway, Jones, Giambattista, Alan P Lightman, all those authors say that the 45° angle...so I am guessing that the 45° must be determine in northern latitudes or something...thats why i thought that maybe the fact that I am located in venezuela must have had something to do...microgravity, etc...

why all those authors obtain 45° while i got 30°??

 

[Dieseltwitch]

Because most of those book don't take into account air resistance. or at least how it pulls it down to Earth over time. most of the books your talking about only use it to see how a bullet slows down over time but doesn't put it in with the angle calculation.
shooting in the north has little to no difference then the south.
what matters (and only in long range shooting... 1000yrds +) is the direction (with the rotation of the Earth or against it).
if you want a really good book to read. type "Understanding Fire Arm Ballistics" into ebay. this guy goes over every thing from barrel whip to how the grains of powder are formed...

 

[hemmi]

Most physics textbooks when introducing the subject ignore the affect of air on moving objects for the sake of simplicity. I find it easier to first understand projectile motion in terms of pure theory, in a vacuum, as it describes will happen in %99.9999999 percent of the universe where there is no air. That way a solid theoretical foundation is formed it becomes even simpler to add on the obstructing concept of air resistance.

 

[tiny-tim]

...but when we did the experiment in the lab we obtain that the best angle (the most distance achived by the metal ball)...was 30º

Hi reinaldo!

Some real physics!

Can you describe the experiment?

In particular, how did you launch the ball, and how did you make sure that it had the same speed at different angles?

And how far did it go, and did it land at the same height as it was launched from?

 

[russ_watters]

If the lab experiment was actually in a lab (ie, a small scale experiment), you really should have gotten an answer nearer to 45 degrees. The velocities would be too small for air resistance to make a difference. Could you describe the experiment?

Was it launched with a spring? When you launch with a spring, the initial velocities are not identical, since the spring has to absorb some of the weight of the ball. Ie, for a horizontal launch, f=ma, but for a vertical launch, f-mg=ma

I would hope your prof actually knew this and wasn't just blowing you off...

 

[reinaldo]

The experiment was made in a Lab with a Small Scale equipment and it consisted of a canon type shooter with a spring, you would lacht the spring and slide the metal ball inside, and the canon was place in an axis with a all the 90° posibles positions, then you would trigger the cannon at the selected angle and we´d measure the height obtain, and the distance obtain in the X axis...we repeated the experiment 15 times in each angle...15°, 23°, 30°, 37°, 45°, 55°, 70°, 80°...the most horizontal distance we got was with the 30° angle...

 

[russ_watters]

In that case, I'd suspect that the weight of the ball on the spring, resulting in an inconsistent launch speed, is what caused what you found.

 

[awvvu]

Also, the optimum launch angle for distance when the projectile lands under its initial height is not 45 degrees, right?

 

[DaveC426913]

I find it easier to first understand projectile motion in terms of pure theory, in a vacuum, as it describes will happen in %99.9999999 percent of the universe where there is no air.

While I agree with your point that it's simpler to ignore confounding factors such as air resistance until you've understood the basics, I think your rationale leaves something to be desired.

In 99.9999999% of the universe, you're not going to encounter gravitational forces that behave as planes (like they do on the human scale, on Earth, where gravity is a force whose direction never changes wrt the object's path). In 99.9999999% of the universe, forces of gravity will act more like points, and ballistic paths will be elliptical rather than parabolic.