Lesson 2: Answers/hints for exercises

  1. Describe a system for locating places on portions of Earth without using latitude and longitude.
    Example: System is comprised of two sets of parallel circles. One set is centered around a line through the earth and intersecting the equator at the Greenwich meridian and the International Date Line; the other is centered around a line that intersects the equator at 90°W and 90°E. Each point on Earth, with the "poles" as exceptions, is an intersection of two of the circles.
  2. Convert the distance 1.6 meters to feet and inches, to the nearest inch.
    Convert to centimeters, divide by 2.54 (number of centimeters per inch), and divide by 12 (number of inches per foot):
    1,600 * 100 / 2.54 / 12 inches
    = approximately 52.5 inches = 4 feet 4.5 inches
  3. How many miles are there in a light year?
    Use 186,000 miles per second as the speed of light and multiply by the number of seconds per year.
    186,000 (mi/sec) * 60 (sec/min)*60 (min/hr)*24 (hr/day) * 365 (days/yr)
    = 5.8657*10^12 miles
  4. Given that the scale of a particular map is 1:1500, what are the dimensions of a map that represents a square whose sides are one mile long?

    The map is a square whose sides are 1/1500 mile long. In practical terms,
    1/1500 mile = (1/1500)*5280*12 inches = 42.24 inches
  5. Given that the scale of a particular map is 1/16 inch : 1 mile, determine approximate dimensions for a map of California.
    Use (no. miles) * (no. inches per mile) = no. of inches
    Actual size and shape of the map is determined by the projection used (to be studied in a later lesson). Suppose, for this example, that we use a rectangle representing extreme north and south borders that are 900 miles apart and extreme east and west borders that are 600 miles apart measured in east-west direction. Then the dimensions of the map will be 900 * 1/16 inches by 600 * 1/16 inches, or, approximately, 56 inches by 38 inches
  6. How many square kilometers are there in one square mile?
    1 mile = (approximately) 1.61 kilometers. So
    1 square mile = (approximately) 1.61*1.61 square kilometers
    = (approximately) 2.592 square kilometers
  7. How many square miles are there in one hectare?
    Convert hectares --> square meters --> square miles
    1 hectare = 100*100 square meters
    = (100/1,610 miles)*(100/1,610 miles)
    = approximately .0038 square miles
  8. Approximately how much time is required for light to travel from the Sun to Earth?
    Using 93,000,000 miles as approximate distance from Earth to Sun and 186,000 miles/second as speed of light,
    time = 93,000,000 (miles)/186,000 (miles/second)
    = approximately 500 seconds = 8 minutes, 20 seconds

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Materials developed by-
Wm. Rundberg
College of San Mateo
1700 West Hillsdale Blvd
San Mateo, Ca. 94402
650.574.6258
rundberg@smcccd.cc.ca.us