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March 29, 2017

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Assume that the Earth is spherical and recall that latitudes range from 0° at the Equator to 90° N at the North Pole. Consider Dubuque, Iowa (42.50° N latitude), and Guatemala City (14.62° N latitude). The two cities lie on approximately the same longitude. Do not neglect the curvature of the Earth in determining the following.

If one could burrow through the Earth and dig a straight-line tunnel from Dubuque to Guatemala City, how long would the tunnel be?

-->I know the answer for above and it is
3072992.8 m..i need help with part b


b)From the point of view of the digger, at what angle below the horizontal would the tunnel be directed?

  • physics - ,

    If the tunnel length is L and the Earth radius is R, the angle below horizontal is
    arcsin [L/(2R)]

    Prove it to yourself by drawing a circular arc and a straight line between the two cities, with the center of the Earth as the center of the arc. A line from the center of the Earth to the center of the straight line (tunnel) forms a right triangle with hypotenuse R, angle A at the Earth center, and one side equal to L/2.

    A = arcsin [L/(2R)]

    Look up R. It is about 6.4*10^6 m
    I get about 29 degrees. .

  • physics - ,

    for L, are you using the answer from part a?? when i use that i get around 14 degrees

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