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Expert: - 9/10/2010


Question
The Sun sets, fully disappearing over the horizon as you lie on the beach,
your eyes 30cm above the sand. You immediately jump up, your eyes are now
150cm  above the sand,  and you can again see the top of the Sun. If you
count the number of seconds  until the Sun fully disappears again, you can
estimate the radius of the Earth. Use the known radius of the Earth to
calculate the time.  radius earth= 6,378,100 meters.  

Please help.  thank you

Answer
Put this in triangle format.

The first triangle has a side that is 6,378,100 m and a hypotenuse that is 6,378,100.1 m.  The second triangle has the same base but a hypotenuse of 6,378,100.15 m.  The near side over the hypotenuse is the cos() of the internal angle.

The difference in these two angles is the same as how far the sun has moved around the earth.  Let them be in degrees.

Take the angle moved and divide by 360 to get the fraction of a day that has passed.  Multiply this by 24 to get hours.  Multiply the answer to the last by 60 to get minutes.  If necessary, multiply the answer to this by 60 again to get seconds.

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Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.

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