physics

posted by .

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?

  • physics -

    The subtended angle between the two cities, measured from the Earth's center, is 42.50-14.62 = 27.88 degrees
    (You can take the difference of the two latitudes since the longitudes are the same.)

    The distance you want is the base of an isosceles triangle with two equal sides R (the earth radius) and apex angle A = 27.88 degrees.

    R = 6370 km

    Tunnel Length = 2*R*sin(A/2)= 3069 km

  • physics -

    thanks

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Geo

    How does latitude and Longitude affect the climate in St.Jonh. I don't get it?
  2. Physics

    Assuming that the Earth is spherical and recalling that latitudes range from 0° at the Equator to 90° N at the North Pole, how far apart, measured on the Earth's surface, are Copenhagen (55.67° N latitude), and Rome (41.90° N latitude)?
  3. Algebra ii

    City B is due north of city A. City A has a latitude of 14.6 degrees N, and city B has a latitude of 47.2 degrees N. find the distance in kilometers between the cities.
  4. physics

    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 …
  5. physics

    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 …
  6. Math

    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 …
  7. Physics

    Assuming that the Earth is spherical and recalling that latitudes range from 0° at the Equator to 90° N at the North Pole, how far apart, measured on the Earth's surface, are Copenhagen (55.67° N latitude), and Rome (41.90° N latitude)?
  8. Geometry

    find the distance between the cities. Assume that Earth is a sphere of radius 4000 miles and that the cities are on the same longitude (one city is due north of the other) Dallas, Texas Latitude: 32* 47' 39" Omaha, Nebraska Latitude: …
  9. ss

    what are latitude and longitude? lines of __________ and lines __________ cross one another. they form a ____________ around the earth. lines of latitude lines of latitude are also called___________ they circle the earth parallel to
  10. Pre-Calculus

    Two cities are due north of each other. One city has a latitude of 32¢ª45'12" and the second city has a latitude of 51¢ª12'45". Assuming that the earth is a sphere with a radius of 4000 miles, how far apart are the two cities?

More Similar Questions