How Does Launch Angle Affect Slingshot Range and Velocity?

[physics_wannabe]

First of all, I just want to take the time and thank anyone who helps me with this, it is greatly appreciated.

Homework Statement

We take a mounted slingshot where you can adjust the launch angle and pull the rubber band back to a set position that is the same everytime. We launched it from 4 angles 10 times taking the mean of the displacement of each angle. This was done for 10,20,30 and 40 degree angles with respective displacements 5.3m, 8.2m, 9.3m and 10.4m. This is all assuming no sources of error such as wind, discrepencies in how perfect the sling was pulled back into the same position each time, etc.

Now this is what is asked:

Determine each angle's initial velocity. Once the initial velocity has been established, develop a relationship between the angle of elevation of the slingshot and each of these:
1) the horizontal range of the slingshot
2) the inital velocity

Reworking the range formula I determined that the respective initial velocities are these 12.3, 11.2, 10.3 and 10.2.

Initial velocity formula I used: v=(Rg/(sin(2θ))^(1/2)

Homework Equations

Now the problem is, how can I determine a relationship when the initial velocities are different? When I first looked at this I thought to myself "wow, this is going to be easy", thinking that I would just create the formulas to determine this information via the angle. But I didn't think about how there would be different velocities with now way of showing a real relationship, at least, that I know of.

The Attempt at a Solution

There is really nothing for me to attempt. I have no idea where to start.

 

[Chi Meson]

If it makes you feel any better, I'm still scratching my head over what the question wants.

The initial velocity (ideally) does not depend on the angle of launch. so the only other way to look at it, is from the "real" world. As the angle increases, the initial velocity decreases a bit due to the fact that the projectile is launched from a slightly higher elevation (some of the sling's work is used to increase the potential energy, and so there is less initial kinetic energy).

Examining the relationship between angle and initial velocity from an energy point of view may be helpful.

 

[physics_wannabe]

Yeah, I wish it made me feel better that everyone I've talked to that is very good with physics have no idea what this question is asking considering this is only engineering physics I. :) This professor's lectures are great, I've learned a lot and he is able to make it interesting and humorous. But then he gives us labs where everything he has taught us is applicable except the questions that are asked of us don't really make any sense. And if you ask him a question all you get is a vague response.

Anyway, so your saying that based on the fact that the sling is elevated more and more as the angle increases that would explain the reason why the initial velocities are decreasing? That would make sense, the thing that confuses me is that at one point I swear he said that the initial height of the sling should be irrelevant. But I will definitely be taking that into account now that you've mentioned it. My lab partner decided to work the entire thing working with energy even though we were never taught any of this yet and he came up with a velocity equation which seems to bring out erroneous information. I plotted the velocities with their respective angles and developed a cubic equation that will calculate the velocity analytically based off the recorded data. We showed our professor both of these approaches and his analogy of what we were doing was something along the lines of "your supposed to be building a tricycle but your building a hummer".. and he claimed we were way ahead of what everyone else was doing but that was all he said lol, so it was kind of misleading. Like, one point is we are doing way too much work and then the next is that we are doing great and much better then everyone else and that we have the problem pretty much licked. This guy loves leaving us confused. This was proven from day one when our syllabus was covered with completely unheard of acronyms which he finally explained. Fortunately the first submission is only the rough draft so I will be submitting what I have and my partners derivations along with your ideas and I will let you know what comments he makes about it (If I can understand the acronyms). If I ever find a definitive answer I will be sure to post a follow-up, and if anyone has any other ideas I would love to hear them.

 

[Chi Meson]

Perhaps he is being deliberately confusing to force some desperate and original thinking? Best of luck to you my friend! At least you aren't alone in that boat.