Your Daily Distraction: Velociraptor Math

October 23 2009 Stephanie Rozek 110
Maple

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A favorite diversion of mine (and of many around the Maplesoft office) is xkcd. Its author, Randall Munroe, bills it as “a webcomic of romance, sarcasm, math, and language.” Since 2005, he’s been entertaining many self-proclaimed geeks with his unique and slightly skewed jokes on technology, computer science, mathematics, and relationships.

I really like the post in which a substitute teacher – hm, Mr. Munroe... - sets a somewhat questionable test for his students. It really speaks for itself:

A few illustrious folks out there (Huaizhi Chen, for example) have taken the time to solve this problem; I’m standing on their shoulders and have used Maple to illustrate the solutions.

The first question is fairly simple. The speed of the velociraptor can be expressed as a simple piecewise function:

Assuming the raptor starts from an initial point of 0, its location at time T is:

The person’s location at time T is:

, where so

By equating the positions of the raptor and the person at time T, we can obtain an expression for the time it took for the raptor to catch the person. I’ve attached the Maple document so you can see the details, but basically, when we solve, we see that it takes about 6.2 seconds for the person to be caught (and in that time, the person ran an amazing 37 meters).

I’ll follow up in a future post with the solution to the 2nd part. Until then, you may want to school yourselves in the ways to survive velociraptor attacks.

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