Problem 202. the fly, the train, the second train, and their Zeno's paradox

Created by Alfonso Nieto-Castanon

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>You have heard this one</w:t></w:r><w:r><w:t>: A train leaves station</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>A</w:t></w:r><w:r><w:t> and travels with constant velocity</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>v1</w:t></w:r><w:r><w:t>. A second train leaves station</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>B</w:t></w:r><w:r><w:t> (at a distance</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>d</w:t></w:r><w:r><w:t>) and travels in opposite direction with constant velocity</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>v2</w:t></w:r><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>What you may have not heard</w:t></w:r><w:r><w:t> is that a fly left station</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>A</w:t></w:r><w:r><w:t> at the same time as the first train (and in the same direction) flying with a constant velocity</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>v3</w:t></w:r><w:r><w:t> (</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>v3&gt;v1</w:t></w:r><w:r><w:t> and</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>v3&gt;v2</w:t></w:r><w:r><w:t> ). When the fly reached the second train it turned around and kept flying in the opposite direction. When it reached the first train it turned around again, and so forth, until its tragic demise (when the two trains collided).</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>The question is</w:t></w:r><w:r><w:t>: what distance has the fly traveled in total (summing all its going and coming back the rails) before meeting its end?</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Your function should take as input the scalars</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>v1</w:t></w:r><w:r><w:t>,</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>v2</w:t></w:r><w:r><w:t>,</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>v3</w:t></w:r><w:r><w:t>, and</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>d</w:t></w:r><w:r><w:t>, and it should return</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>s</w:t></w:r><w:r><w:t> the total distance traveled by the fly (up to 1% error allowed)</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

You have heard this one: A train leaves station A and travels with constant velocity v1. A second train leaves station B (at a distance d) and travels in opposite direction with constant velocity v2.What you may have not heard is that a fly left station A at the same time as the first train (and in the same direction) flying with a constant velocity v3 ( v3&gt;v1 and v3&gt;v2 ). When the fly reached the second train it turned around 
and kept flying in the opposite direction. When it reached the first train it turned around again, and so forth, until its tragic demise (when the two trains collided).The question is: what distance has the fly traveled in total (summing all its going and coming back the rails) before meeting its end?Your function should take as input the scalars v1, v2, v3, and d, and it should return s the total distance traveled by the fly (up to 1% error allowed)

Solve

Solution Stats

102 Solutions
61 Solvers

Last Solution submitted on Jan 15, 2022

Last 200 Solutions

Problem Comments

1 Comment

1 Comment

Rafael S.T. Vieira on 15 Sep 2020

It's seems that even if we consider that the fly is always colliding with the same train (instead of zig-zagging between trains), the results are always the same.

Problem Recent Solvers61

Problem Tags

math

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 202. the fly, the train, the second train, and their Zeno's paradox

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers61

Suggested Problems

More from this Author38

Problem Tags

Community Treasure Hunt

Problem 202. the fly, the train, the second train, and their Zeno's paradox

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers61

Suggested Problems

More from this Author38

Problem Tags

Community Treasure Hunt

Players