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19. When the Sun first disappears while lying down, your line of sight to the top of the
Sun is tangent to the Earth’s surface at point A shown in the figure. As you stand,
elevating your eyes by a height h, the line of sight to the Sun is tangent to the Earth’s
surface at point B.
Let
d
be the distance from point B to your eyes. From Pythagorean theorem, we have
22
2 2
2
()
2
dr
r
h
r
r
h
h
+=+
=+
+
or
2,
h
h
where
r
is the radius of the Earth. Since
rh
5
, the second term can be
dropped, leading to
2
2
h
≈
. Now the angle between the two radii to the two tangent
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 Spring '06
 Stoler
 Physics

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