There are many reasons why students should go to university and do a mathematical (or mathematically related) degree. A good reason is because of interesting and stimulating  investigations. Take for example my dissertations. For my BSc I looked at pendulums and created  working models of inverted pendulums. For my MSc dissertation I looked into splashes, which included looking at the mechanics of stone-skipping.

Stone Skipping

My MSc dissertation can be downloaded here.

Splashes are a very interesting area of fluid dynamics. My MSc looked at the some problems relating to the impact of solid bodies on fluids. The most fun application of this is standing at the beach playing skipping-stones (of course there are more serious examples such as maritime structures and bouncing-bombs). Let us look at a stone hitting the water surface,

The equations of motion for a circular stone are,

It is interesting to see under which conditions, for the parameters, we can achieve the stone skipping effect. An example of this is shown below.

Clearly though, the only question anybody would be interested in is how to get more skips! Fixing the tilt of the stone to be about 20 (since this gives a good range of throwing angle) I investigated. I created the graph below which seems to show that the number of skips is (approximately) a linear relationship with the initial speed the stone is thrown at. This means if you want to achieve more skips then throw it with a bit more speed! Common sense really.