My LEGO Nexus Organization

(http://us.mindstorms.lego.com/en-us/community/NXTLog/showmedia.aspx?id=949e415a-decd-45d2-ab1e-ddc40e5a9780&width=350&height=263)
I recently entered a contest with my greatest creation yet! Using my Mindstorms NXT set, I took up a challenge presented by the LEGO Mindstorms team to build a project which utilizes a sensor (for the NXTLOG Sensor Overload Competition). This project took me almost a month and a half to complete, and I am extremely proud of it. Consisting of two motors, one ultrasonic sensor, the Intelligent brick, lots of LEGO pieces, and a very complex program, the Ultrasonic Sensor calculates the angle it needs to launch a 2x2 LEGO brick in order to get it to land in a LEGO box a distance away (distance measured by Ultrasonic Sensor). I won't say more than that about the creation here because there is already a detailed description here: http://us.mindstorms.lego.com/en-us/Community/NXTLog/DisplayProject.aspx?id=1e0a933e-2a18-4e8f-9a25-b535033de62f (http://us.mindstorms.lego.com/en-us/Community/NXTLog/DisplayProject.aspx?id=1e0a933e-2a18-4e8f-9a25-b535033de62f). If you don't have time to read all the description, please at least watch the video! Thank you for taking the time to check out my project. :-)

This is a truly elegant design, CC. I may have to rebuild it for use with dog treats!!
Ultimate LEGO Launcher = TOTAL WIN!!

This sounds very cool. =) I'll look at the video and description later, but just from the brief description, this sounds extremely cool, and is something that would be very interesting to see in action. =)

Oh, and if you guys have time, could you perhaps rate it (http://us.mindstorms.lego.com/en-us/Community/NXTLog/DisplayProject.aspx?id=1e0a933e-2a18-4e8f-9a25-b535033de62f) on the NXTLOG? Thanks!  ;D

MsRowdyRedhead,
Thanks! And thanks for the comment on the NXTLOG too.  :) Lol, that would be funny!

Blade,

Great! I hope you enjoy it, and thanks for checking it out!  :)

Rahkshi8000,

Thank you very much!! I'm pursuing a career in engineering or the scientific field, but first I must conquer highschool.  :)

You seem to have the steps correct for solving for velocity, but you said you were solving for theta. The range equation solved for theta is used in the programming, while the range equation solved for velocity was used by me to calculate the velocity of the LEGO brick.

I solved for theta, which was used in the programming, by:

1. Multiplying both sides by "g"
2. Dividing both sides by v^2
3. Removing sine from one side by finding the arcsine of the other side (finding the arsine of one side is the same as finding the sine of the other)
4. Dividing both sides by 2

The picture shows the equation solved for theta:
(http://us.mindstorms.lego.com/en-us/community/NXTLog/showmedia.aspx?id=df7daf7d-28b3-451e-9941-bc5c88fb5d07&width=350&height=263)
 
I also needed to solve for v (velocity), which allowed me to calculate the velocity of the LEGO brick:

1. Multiplying both sides by "g"
2. Dividing both sides by "sin(2θ)"
3. Finding the square root of both sides

This picture shows the equation solved for velocity:
(http://us.mindstorms.lego.com/en-us/community/NXTLog/showmedia.aspx?id=afd8154f-6e53-47e9-9826-dcc48c0f99cd&width=350&height=263)

Indeed, it was no coincidence that I picked a 45 degree angle for finding the velocity of the LEGO brick.  :) In fact, before I even learned about the range equation in physics, I was using a formula that was made especially for cases in which you are always launching at 45 degrees. The equation is surprisingly simple, although it makes total sense that it can be reduced that much when theta isn't a factor. Check it out:

(http://upload.wikimedia.org/math/f/4/e/f4e89b74ea38b99c833aff04ff060e5a.png)

Multiplying both sides by g and finding the square root, you come up with: velocity= square root of g*d.

I'm assuming you don't have the NXT-G programming language used by most Mindstorms users... if you did, you can easily download my program and check it out. I can post a few pictures if you'd like.

Thanks again for your compliments and interest in my project. Not everyone knows enough in physics/math to understand my project to the amount I would like them to, so I enjoy explaining my project to those who do.  :) If you have any questions, or my explanation is too confusing, please let me know.  ;D

Thanks again everyone!! Your comments made my day(s).  :)

Perhaps you mean trebuchet, Legodac? Or perhaps Tribochet means something I am unaware of... thank you for your compliments, they are very encouraging. And thanks for the warm welcome.  :)

I have always thought that architecture would be fun, Rahkshi8000, and have even considered it. However, I am even more fascinated by physics and mechanical engineering. Do you own any of the LEGO Architecture (http://architecture.lego.com/en-us/default.aspx?icmp=COFranchiseUSArchitecture) sets? I think they are awesome, but unfortunately do not own any. They would be epic to have on your desk at work, especially if you work for LEGO.

Great creation! I'm not the most interested in Mindstorms creations, but as I said before; great creation! Now only if I could understand those formulas...