The Athletics Track
We take for granted that our standard 400 metre running tracks provide 100 m straights, and staggered starts for distances like the 200 m sprint and the 400m hurdles, but who works it all out for us, and how ... ?!
This is a " pi x D " and " pi x r ² " - based set of problems which should get most students' attention readily. It's ideal for analysis by Spreadsheet, taking the length of the straight as the initial variable. It is also a nice revision exercise in Algebra manipulation.
A If each straight and each bend is to have an inner length of 100 metres, then how long and how wide should the ' field ' area be?
B The 200 m has to have a set of 'staggered' starts, so that those running in the outer lanes end up running the same distance as those in the inner lane.
By how much should each lane be set forward of the lane inside it ?
You will need to decide how wide each lane should be, first...
C The 'staggers' for the 400 m will need to take account of having to run both bends ...
If we relax the condition that the straights and the bends must both be of equal length, then a wide range of shapes become possible...
D Which designs ( as represented by their bend radius ) maximise / minimise the enclosed areas of 'field' ?
E What effect does the radius chosen have on the area of track itself ?
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