Sailors on early ships had no real way of knowing how fast they were traveling and how far they had gone in a specific period of time. So a system of measuring was devised, using a log of wood.
The log had a weight tied to one end and a long rope attaching the other end to the stern, or back of the ship. The log floated behind the ship a certain distance, the length the rope was let out.
Then, as the ship sailed faster, the rope was let out more and more to keep that length of rope the same. In that way, sailors were able to judge the ship’s speed by figuring out how much rope they let out.
Later, this rope was tied in knots, at equal distances apart. To figure out the ship’s speed, a sailor need only count how many knots he let out. So “knots” came to be used as a measure of a ship’s speed.
At sea today, “knots” have a specific measure. One knot is equal to one nautical mile (6,076 feet), which is slightly longer than a mile measured on land (5,280 feet).
The world’s fastest ship is a 112-ton U.S. Navy test warship, the SES-100B, which when tested in 1976, reached a speed of 88.88 knots, or 102.35 mph!
I think that the answer given is simply wrong. I think that the sailors would let out the rope fast enough to keep the float from being pulled by the rope and that this exercise would continue for a set time, perhaps 5 minutes. From that start, simple math would solve for the actual speed. Likely the knots were splices between lengths of rope of a known length … perhaps each one nautical mile (1852 meters) long. Extra slack in the rope could be accounted for by subtracting the number of seconds between the time the rope stopped being fed out and the time the float tipped in the water. This time would be subtracted from the over-all time to give the exact time that the rope was at proper tension.
How do you let out more rope to keep the length of rope the same? It comes from the number of equally-spaced knots that were paid out, during a fixed time period, on a long piece of cord attached to a “chip log” (a sort of sea anchor) that had been thrown overboard.