Rat rod vs Lambor

Wednesday, February 3, 2016

Math barbie project #1

Our wonderful math teacher, Mr. Ockness came up with the idea to improve our familiarity with quadratic equations by making us investigate bungee jumping. This project is about bungee jumping a Barbie doll from a given height and making the jump as thrilling as possible by getting the doll close to the ground. The approach that our group is going to take on this project is to find a pattern such as how much the length of the jump increases. In other words, we are currently trying to find the slope of the graph. Here are some statistics that might help us run realistic trials and determine the pattern of the quadratic equation.

Barbie weight: 89.1 g
Barbie height: 30 cm
Length of rubber band (not stretched): 7.5 cm

In our first trial, we jumped the barbie from a height of 1.92 meters found out that it will take 14 rubber bands for the barbie to jump and almost hit the ground by 2 cm. By only judging by this trial, the x intercept of the quadratic equation is only 0 as it is a multiple root equation also the maximum value for the graph is 192, a quadratic equation with a positive slope is usually not able to have a maximum value. But in this case, as the maximum height of the jump is 192 cm, the Barbie doll will not be able to bounce up and go in to heights beyond that. Cause if it did, it would either be that Mr. Ocksness bought some extremely high quality rubber bands, or that our project has just defied the laws of physics.

The graph that I could come up with by only taking this trial into consideration is this:
( up to this point, we really don't know what x and y really stands for but this graph is just a reflection of what happened)

The first graph that I came up with is a curve that goes down and back up exactly where it came from and therefore is identical to the y axis. I have marked the x intercept which is (0,2) and the maximum value of y (0,192). I don't think this graph is entirely correct as  this graph was purely made by looking into only one trial and as we haven't really found a pattern yet, we don't have any guesses of the slope of the graph and that is why there is no visible curve to it.


The second graph is also just an estimation/hypothesis judging by the statistics of the first trial. The equation of the graph is y=x^2 the reason why I estimate that the graph would look something like this is because I figured out the 14^2 is 196 and as 196 is extremely close to 192 cm I figured out that the real quadratic equation could look like something like this. What y stands for in this equation is the height of the jump, and what x stands for is the amount of elastics. Another thing that proves that this graph might be something like the real one is that if u input 192 into the value of y, 192=x^2 the value of x will turn out to be 13.88 which is pretty close to 14. And I think that for the graph to be exactly target, I think that I can adjust the 0.12 difference in value by adding a y intercept of -4
And if I do that the graph would look like this;

by looking at it in such a big scale, the y intercept of -4 does not make such a big difference, but if we plug the x and y values in to the equation of y=x^2-4, the values match out perfectly. And as we now have some sort of hypothesis that is on the right track, we are able to test this equation in different heights and make certain adjustments for our final project.

Plans for next class:

1. do two more trials in different heights
2. test out how gravity works in different heights
3. make adjustments to our current equation

Here is a video of our first trial:

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