Thursday, March 4, 2010

Final Project: The Related Rates Time Machine

Group 4
Nom de plumes: babar, WinnPlot, Tubby.

The purpose of this Final Project was to create a unique related rates problem from a real world situation and then solve this problem, thus expanding our knowledge of related rates, and their application in the real world.

image source:

Young Freddy Newton was trying to make it big in the stock market, and decided to build a time machine (see image) so he would be sure to buy the right Stock. Unfortunately the time machine malfunctioned sending Freddy into a ripple of time and space and landing him in the land of dinosaurs with only a bendy straw in his possession. Freddy was so thirsty upon arrival but could not find any clean water. Finally after three weeks of wandering the land aimlessly Freddy came upon a bowl, that we assume is a half-sphere filled with prehistoric sludge. It had a volume of 355cubic centimeters and a radius at the top of 6.75centimeters. It takes him 22.65 seconds to consume the sludge. Freddy uses his handy dandy bendy straw to drink the sludge for sustenance. We are going to assume that he drinks at a constant rate. Below is a video of this event:

So, the related rates question is:
If a semi-sphere with a volume of 355 cubic centimeters filled with prehistoric sludge takes 22.64 seconds to consume what is the rate, in minutes, at which the height of sludge in the bowl is changing at the moment when the sludge is at 2 centimeters?

Here is a hyperlink to the solution:

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