Question #ed863

1 Answer
Mark C.
Jan 17, 2018

OK, we can, but it’s not very easy.

Explanation:

Firstly, there is the definition of an arc-second. A degree is #1/360# of a circle, a minute is defined as #1/60th# of a degree and a second (or arc-second) is #1/60th# of a minute. 1 arc-second is thus #(1/3600)^@# We need this in radians, and 1 rad = #(360/(2pi))^@# so an arc-second = #1/3600 xx (2pi)/360# rad so 1 arc-second = #4.848 xx 10^-6# rad

Next there is a very simple link between arc length, s (which we will assume to be equal to the diameter of the nickel), the radius, r (the distance we need to find) and the angle in radians, #theta#. It is just #theta = s/r# so #r = s/theta#

Finally, the diameter of the nickel is 21.21mm (had to google that, I’m British) which we convert to #2.121 xx 10^-2#m as we want an answer for r in m.

#r = s/theta = (2.121xx10^-2)/(4.848xx10^-6) = 4,375# m

You could criticise this result as the diameter of the nickel is actually a chord, not an arc, but I suspect it makes little difference to your answer.

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