HELP WITH MATH EXPLORATION USING TRIG/CORRELATION

[fairyflaunt]

I'm having trouble with expanding on my ME topics and don't know what to include  My first idea was to use statistics to find the correlation between the height of children and their parents, but I'm not sure what to do to make it more substantial. I'm facing the same problem with my second idea, where I wanted to use trig to find the optimal angle for swimmers to plunge from the plunging block. My teacher said to find a function for that but I'm still very confused as to how to go about doing a whole ME on that since it also includes projectile motion.

My proposal is due in a week and I would really appreciate the help!!

[kw0573]

First idea: How could analyzing this possible relationship be useful, for example to the police? If one child were to be lost in an amusement park, could we use the height to contact families as efficiently as possible? Try come up with other useful scenarios so you can apply what you find about the heights' correlation.

Second idea:  Do you know projectile motion? If you are comfortable with the physics, perhaps you can extend your exploration to the entire swim, rather just the plunge. You can look at ways to conserve time, energy (eg in a heat, the swimmer wants to conserve energy).

You may also consider non-problem-oriented math IAs. For example you can study a theorem, properties of integers/sequences, or some general applications of mathematics such as in cryptography.  The IA does not have to be strictly doing some number crunching to get a numerical answer.
 

[IB Math Helper]

With regards to the correlation in height between parents and children, it's important to subset the data by gender (fathers and sons, mothers and daughters) and by age (how old are the children you want to consider? Consider adult children themselves if you're able to get data). Consider the R (correlation co-efficient) and R^2 (co-efficient of determination) values and explain their meaning. Once you have your data, consider the factors that could affect height of children (e.g. nutrition). Look up some studies that focus on height of children over time (go to a librarian and ask them for help on how to find these journal articles). This latter part would reflect personal engagement.

For your second idea, as kw0573 said, you need to know the physics. To collect data you might have to record video and analyze it with some physics theory. If you're interested in projectile motion, you should consider something related like angry birds where you want to study the angles of release in order to optimally hit your target. This is just one of potentially many ideas. Basically, if swimming doesn't work, consider some other ideas that involve projectile motion (again, knowing the physics helps greatly).

[fairyflaunt]

thanks so much for the help!! I was wondering if doing an ME on using calculus and optimization to find the optimum volume of a can that would cost the least. does that show more understanding and application of math?

[kw0573]

It's hard to judge your understanding and application of math just from the topic (otherwise we have the absurd situation of people just submitting a topic without writing anything). I will say that optimization cost is a fairly common topic so you may have to do/think more than others to score a very good mark.