Universe
Universe
11th Edition
ISBN: 9781319039448
Author: Robert Geller, Roger Freedman, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 1, Problem 22Q
To determine

The exponents and the way they are used in powers-of-ten notation.

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BACKGROUND An ingenious solution to the Earth's circumference occured in 230 BC. Eratosthenes, a Greek geographer, mathematician, music theorist, poet, astronomer, and philosopher, was reading in the Library of Alexandria when he noticed an account for a deep well near Syene (now Aswan), some distance to the south (800 km) in which at high noon on the longest day of the year the bottom of the well was fully illuminated by the Sun. Eratosthenes exclaimed "Ah-ah!" (or something like that), "I can solve for the circumference of the Earth!". In his mind's eye, Eratosthenes could see that at Syene, at the moment when the bottom of the well was fully lit, the Sun must have been at the Zenith (directly overhead). Yet he knew that at the same moment in Alexandria vertical objects (like a tower, pole) cast shadows. Here is the experiment perfomed by Eratosthenes (see the picture below). • He erected a vertical pole at Alexandria (A) and measured the angle of its shadow at the moment when the…
It takes 23 hours 56 minutes and 4 seconds for the earth to make one revolution (mean sidereal day). What is the angular speed of the earth? Submit Answer Tries 0/12 Assume the earth is spherical. Relative to someone on the rotation axis, what is the linear speed of an object on the surface if the radius vector from the center of the earth to the object makes an angle of 61.0° with the axis of rotation. The radius of the earth is 6.37×103 km. Submit Answer Tries 0/12 What is the acceleration of the object on the surface of the earth in the previous problem? Submit Answer Tries 0/12
33. If you are at the top of a tower of height h above the surface of the earth, show that the distance you can see along the surface of the earth is approximately s = v2Rh, where R is the radius of the earth. Hints: See figure. Show that h/R = sec 0 – 1; find two terms of the series for sec 0 = 1/ cos 0, and use s = RO. _Thus show that the distance in miles is approximately v3h/2 with h in feet. Rİ
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