Question

Question #ed863

Answer 1

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.