30 lines
1.0 KiB
TeX
Executable File
30 lines
1.0 KiB
TeX
Executable File
\documentclass[
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solutions,
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singlenumbering,
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nopagenumber
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]{../../resources/ormc_handout}
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\usepackage{../../resources/macros}
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\title{Warm-Up: Travellers}
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\uptitler{\smallurl{}}
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\subtitle{Prepared by Mark on \today}
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\begin{document}
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\maketitle
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\problem{}
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Four travellers are on a plane, each moving along a straight line at an arbitrary constant speed. \par
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No two of their paths are parallel, and no three intersect at the same point. \par
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We know that traveller A has met travelers B, C, and D, \par
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and that traveller B has met C and D (and A). Show that C and D must also have met. \par
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\begin{solution}
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When a body travels at a constant speed, its graph with respect to time is a straight line. \par
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So, we add time axis in the third dimension, perpendicular to our plane. \par
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Naturally, the projection of each of these onto the plane corresponds to a road.
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Now, note that two intersecting lines define a plane and use the conditions in the problem to show that no two lines are parallel.
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\end{solution}
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\end{document} |