Problem: 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 1/21600 of the Earths circumference through the poles. A ships 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 ships 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 league is defined as 3 nautical miles. The Mariana Trench, with a depth of 35798 feet, is the deepest point in the ocean. How many leagues deep is this?

FREE Expert Solution

We have to convert the Depth of Mariana Trench from feet to league units.


We can solve this problem through dimensional analysis by using these conversion factors.

1 league = 3 nautical miles

1 nautical mile = 1/21600 of earth’s circumference from poles

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Problem Details

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 1/21600 of the Earths circumference through the poles. A ships 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 ships 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 league is defined as 3 nautical miles. The Mariana Trench, with a depth of 35798 feet, is the deepest point in the ocean. How many leagues deep is this?

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Our tutors have indicated that to solve this problem you will need to apply the Dimensional Analysis concept. You can view video lessons to learn Dimensional Analysis. Or if you need more Dimensional Analysis practice, you can also practice Dimensional Analysis practice problems.

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