physics

I’ll be back.. I mean I am back.

Greece was great. Check out the Flickr stream for shots of Mykonos, Delos, Athens, and Edinburgh. I just uploaded all of the raw shots, so there are some repeats and blurry photos. Hope to get those cleaned out. Great experience!

The answer to the burning question

Does the snail reach the horse?

In order to solve this question we have to come up with a differential equation to express the velocity of the snail relative to the floor. This is given by:

Vsnail is the velocity of the snail relative to the rubberband and Vhorse is the velocity of the horse relative to the ground. Xsnail is the position of the snail which we are trying to determine. L is the starting length of the rubber band. Here the position of the snail with respect to time is dependent on the snail’s velocity on the band, and the velocity of the horse. One caveat however, the term with the horse’s velocity must include the initial band length (L), plus the location of the horse after a certain amount of time (Vhorse + t).

We need to find a solution to the differential above as:

How do we find the solution?

Simple! Separation of variables! And a little calculus… lets skip the details and…

Lets try:

To check… lets take the derivative of the function with respect to t and plug it back into our original equation:

And we get:

Bingo!

Now lets take our solution and solve for when the horse and the snail meet, ie.:

Thus,

And solving for t we get:

Which is the time at which the snail and horse finally shake hands.

But how long would this take?

Well lets put some approximate parameters into the equation.

Using the numbers above we get seconds! That’s with the world’s fastest snail too! This converts to  2.6×10^3030 years.

Just how long is this? Well the universe supposedly has been around for 13 billion years, or 1.3×10^10. The US Budget deficit is now over 9 trillion, or 9×10^12. Even these numbers, which seem almost incomprehensible to us, pail in comparison to the journey of our two patient animal friends.

In conclusion, if you’re ever feeling down in the dumps, just remember the snail.

This week I’ll be traveling to Greece and staying in the islands of the Mediterranean. Should be a wonderful time and I’ll return with lots of great photos. Anyway, before I go I leave you with a question from Christoph Schiller’s excellent work. Some of you that know me may have already heard this one before, but to the first person to answer without cheating I’ll send a prize. Honest.

The Snail and the Horse

Imagine a rubber band that is attached to a wall on one end and is attached to a horse at the other end. On the rubber, near the wall, there is a snail. Both the snail and the horse start moving, with typical speeds - with the rubbed band being infinitely stretchable. Can the snail reach the horse?

I’ll post my solution when I return. Enjoy!