After painstaking hours in my science world [with hacked items... I need my resources] I've finally deduced what I believe to be at least a short range [short range in scope of the entire minecraft world...] equation for how far one will travel in a minecart from a ramp of a given height. This is by NO means a finished project. I've just come to a point where I need feedback.

The formula goes as follows: [Just as a given... incase you didn't understand, all distances are in blocks for now, but could technically be meters.]

When you build a ramp, it becomes the shape of an isocelese right triangle with two 45 degree angles. The base MUST = the height.

The ramp down [hypotenuse] is always equal to the base [or the height] times the square root of 2.

Basically, X in the equation is base(sqrt(2) <- The hypotenuse.

The equation goes as follows:

[s][.006450881x^3]+[-(.5027315948x^2)]+[17.41144133x]+[32.18798644] = Distance[/s]

I think a more intuitive equation would have to be (43.56235216) * (x^.5656)

This was the result of performing a power regression on collected data, rather than a cubic or quadratic regression. The equation will probably be more accurate, and less cumbersome this way. Because my knowledge of calculus is limited, I used a TI-84 Plus Silver Edition calculator to perform the regressions on the data which I input. After trying many I decided that the graph would best resemble a power regression [though this is debateable...].

Here's my data, hopefully some of you guys have graphing calculators:

**Code:**Length of Ramp | Total Distance before stopping

2(sqrt(2)) | 78

3(sqrt(2)) | 97.5

4(sqrt(2)) | 114.5

5(sqrt(2)) | 132.5

6(sqrt(2)) | 148.5

7(sqrt(2)) | 161.5

8(sqrt(2)) | 174.5

9(sqrt(2)) | 185.5

10(sqrt(2)) | 196.5

11(sqrt(2)) | 205

15(sqrt(2)) |237

For example: Plugging in 11(sqrt(2)) to x [in the equation] you will recieve a value of 205.71. This is how many blocks (after coming off the ramp) the cart will travel. After testing this, the cart did indeed travel 205, and a little bit more, blocks.

Just to clarify, to build a ramp with a base of 11 looks like this [The red dot is where you place the cart, at 0 Velocity: (Image changed to a link for the sake reducing this giant post size...)

https://redcdn.net/ihimizer/img301/6930/minecarts.png-----------------------------------------------------------------------------------------------------------------------

As you can see, I'm not very skilled with cannons as of yet...

I'm gonna hypothesize that this equation should be guaranteed accurate to ramps about 20 blocks in height. Any more than that and you'll probably see deviations of around 10 or so blocks. I only tested up to ramps around 18 blocks in height.

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