SOLUTION: In the city of San Miguel on the island of Cozumel, Mexico, there is a museum with a room devoted to pirates and sailing ships. One of the displays shows a log chip - a small tri
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Question 1189590: In the city of San Miguel on the island of Cozumel, Mexico, there is a museum with a room devoted to pirates and sailing ships. One of the displays shows a log chip - a small triangular, weighted device used by fifteenth- and sixteenth-century sailors to measure speed. The log chip was tied to a rope that was wound up on a reel. The sailors tied evenly spaced knots in the rope. They would then throw the rope overboard and the weight of the log chip would allow the rope to unreel as the boat moved along. The sailors would allow it to unreel for 30 seconds, timed with a sand hourglass. They would then haul the rope in and count the number of knots that had been reeled out. This number was the speed of the boat in knots (nautical miles per hour). If one nautical mile is 6076.10333 feet (one minute of arc of the earth’s circumference), how many feet apart are the knots?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the boat drops anchor at point A.
one end of the rope stays at that point.
the other end of the rope is where the rope is grabbed. this is at point B.
this happens after 30 seconds have elapsed.
the length of the rope from point A to point B is measured.
if the boat was traveling at 1 knot, then the boat was traveling at a speed of 1 nautical mile per hour.
1 nautical mile is 6076.10333 feet.
1 hour is 3600 seconds.
if the boat was traveling at 1 knot, then it would have traveled 6076.10333 feet in 3600 seconds.
since the boat was traveling for 30 seconds then the boat traveled 30 * 6076.10333 / 3600 = 50.63419442 feet.
that would be the length of the rope after 30 seconds.
consequently, each knot on the rope would have to be 50.63419442 feet from another knot on the rope.
assuming that is good, then the number of knots on the rope should be giving the sailors a good idea of how fast they were going.
assuming the boat was traveling at 4 knots, then the boat was traveling at 4 nautical miles per hour.
4 nautical miles per hour is 4 * 6076.10333 feet = 24304.41332 feet.
multiply that by 30/3600 to get 202.5367777 feet.
divide that by 50.63419442 and you get 4 knots.
i used internally stored numbers.
these are rounded to maybe 15 decimal places.
if you use display numbers, they are rounded to maybe 8 decimal places.
my numbers came right on because i used internally stored numbers.
if you tried it with displayed numbers, you might be a little off, but not by much.
most likely the sailors weren't able to get the accuracy shown here, so their speeds were approximate based on how accurately they could measure the distance between knots on the rope.
since the sailing ships of the day probably couldn't do more than 4 or 5 knots, then the maximum length of the rope was probably something less than 300 feet.
let me know if you have any questions.
theo
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