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HINT:Lets consider first what the question is asking.
The question is asking for the earth year during which Supernova exploded.
HINT:What information does the problem give us?
The problem tells us how many arcseconds from the center of the star's remnant the knot that we have been analyzing has traveled. From the previous calculations, we can also determine the number of arc-seconds that the knot travels per year.
HINT:What is the relationship between the information given and the
information needed?
The elapsed time during which the knot traveled a given number of arc-seconds is equal to
t = #arc-seconds traveled * years/#arc-seconds traveled
Year of explosion = Current date - t
HINT:What information do we need to plug into the relationship?
arc-seconds traveled = 100 arc-seconds
years/#arc-seconds traveled = 10 years/3 arc-seconds
HINT: Are we going to need to convert the units of any of the information that
we have gathered?
Let's use unit analysis:
t(km) = #arc-seconds traveled(arc-seconds * (years/#arc-seconds traveled)
All units cancel except for years, so we do not need to convert any units!
HINT:Plug all of the information in to the final calculation!
t = 100 arc-seconds * 10 years/3 arc-seconds = 330 years
date = 2000 CE - 330 years = 1670 CE

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