In 1906 Kennelly developed a simple formula for predicting an upper limit on the fastest time that humans could ever run distances from 100 yards to 10 miles. His formula is given by t equals. 0588 s Superscript 1.125 where s is the distance in meters and t is the time to run that distance in seconds. a. Find Kennelly's estimate for the fastest a human could possibly run 1606 meters. tequals nothing seconds (Round to the nearest thousandth as needed.) b. Find StartFraction dt Over ds EndFraction when sequals20 and interpret your answer. StartFraction dt Over ds EndFraction almost equals nothing sec/m (Round to the nearest thousandth as needed.) When the distance is 20 meters, this rate gives the number of seconds per meter ▼ by which the fastest possible time is increasing. by which the fastest possible time is decreasing. that the fastest human could possibly run.

Question

Mathematics

Quintin

3 December, 06:28

In 1906 Kennelly developed a simple formula for predicting an upper limit on the fastest time that humans could ever run distances from 100 yards to 10 miles. His formula is given by t equals. 0588 s Superscript 1.125 where s is the distance in meters and t is the time to run that distance in seconds. a. Find Kennelly's estimate for the fastest a human could possibly run 1606 meters. tequals nothing seconds (Round to the nearest thousandth as needed.) b. Find StartFraction dt Over ds EndFraction when sequals20 and interpret your answer. StartFraction dt Over ds EndFraction almost equals nothing sec/m (Round to the nearest thousandth as needed.) When the distance is 20 meters, this rate gives the number of seconds per meter ▼ by which the fastest possible time is increasing. by which the fastest possible time is decreasing. that the fastest human could possibly run.

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Ian Cain · Answer 1

Answer / Step-by-step explanation:

(1) Given t = 0.0588s ¹.¹²⁵

where s is the distance and t is the time to run that distance.

The second portion asks us to find the derivative of the equation when our s value is equal to 20 and interpret.

(2) First, we try to convert the unit from miles to meters

Therefore, 1 mile = 1609 meters

Then,

t = 0.0588 (1609) ¹.¹²⁵

=238. 09

This gives us the instantaneous rate of change of seconds between every 20 meters ran.

The last portion asks us to compare this estimate to current world records. And have they been surpassed?

As of today, the fastest official record for a standard mile is held by a man from Morocco named Hichan El Guerrouj. The time was recorded at 3.43 minutes in Rome, Italy on July 7th, 1999.

Now, keep in mind that this is almost a full minute slower than the estimated time. However, how do these projections hold up against Usain Bolt, the man that is considered the fastest man in the world?

Although, Usain Bolt does run long distances, he holds records in nearly every sprinting event that he has ever competed in.

Hence, Kennelly's estimate for the fastest mile is 238.09

(3) Now, noting that since dt / ds = 0.0588 (1.25) s ⁰.¹²⁵

Then,

dt / ds I 100 = 0.0588 (1.25) (20) ⁰.¹²⁵

= 0.1176