Chapter 1, Problem 1.115CP

Distances over land are measured in statute miles (5280 ft), but distances over water are measured in nautical miles, where 1 nautical mile was originally defined as 1 minute of arc along an Earth meridian, or 1/21,600 Of the Earth’s circumference through the poles. A ship’s speed through the water is measured in knots, where 1 knot = 1 nautical mile per hour. Historically, the unit knot derived from the practice of measuring a ship's speed by throwing a log tied to a knotted line over the side. The line had a knot tied in it at intervals of 47 ft. 3 in., and the number of knots run out in 28 seconds was counted to determine speed.

(a) How many feet are in a nautical mile? How many meters?

(b) The northern bluefin tuna can weigh up to 1500 pounds and can swim at speeds up to 48 miles per hour. How fast is this in knots?

(c) A league is defined as 3 nautical miles. The Mariana Trench, with a depth Of 35,798 feet, is the deepest point in the ocean.

How many leagues deep is this?

(d) By international agreement, the nautical mile is now defined as exactly 1852 meters. By what percentage does this Current definition differ from the original definition, and by what percentage does it differ from a Statute mile?