Dear akbsmith,
If the man were to walk entirely around the equator, then the top of
his head would trace a circle whose radius is six feet greater than
that of the equator. In the meantime, his feet would follow the
equator itself.
First, let's consider the length of the equator, which is the circle
around the widest part of the earth. We know from earth measurements
that the equator has a radius of 6378.5 km or 6378500 m.
wikipedia: Earth Radius
http://en.wikipedia.org/wiki/Earth_radius
wikipedia: Equator
http://en.wikipedia.org/wiki/Equator
We also know that the ratio of a circle's circumference to its radius
is twice pi. Thus, the length of the equator in meters is calculated
as follows.
6378500 * 2 * 3.14159 = 40077263
Now let's see what difference the man's height would make. There are
12 inches to a foot, and an inch is exactly 2.54 cm or 0.0254 m, so
the man's height in meters is the following.
6 * 12 * 0.0254 = 1.8288
The radius of the circle traced by his head is therefore
6378500 + 1.8288 = 6378501.8288
and the circumference of this circle is the following.
6378501.8288 * 2 * 3.14159 = 40077275.1207
So the difference in meters between the length of the equator and the
length of the circle traced by the top of the man's head is
40077275.1207 - 40077263 = 12.1207
but we want only one quarter of that, so the final answer is
12.1207 / 4 = 3.0302
meters.
You mention radians, but those can only be used to measure angles.
Both the man's head and his feet travel exactly pi/2 radians, since
they cover the same arc of the equator.
To convert 3.0302 m back into imperial measurements, we divide by
0.0254 m to obtain
3.0302 / 0.0254 = 119.3
inches. That's the same as 11 feet and 11.3 inches.
If you find my answer to be incomplete or inaccurate in any way,
please post a clarification so that I have a chance to meet your needs
before you assign a rating.
Cheers,
leapinglizard
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