Quote:
Originally Posted by Crumpp
|
Come on, Achilles and the Tortoise story is very simple.
Sum of time=1+0.5+0.25+0.125+........ is limited, will never bigger than 2.
of course, Achilles can't over take tortoise WITHIN 2 seconds because tortoise is some distance ahead of Achilles in the beginning.
In ancient time, people didn't know the property of "infinite series", so they were puzzled. They drew the conclusion that Achilles would never overtake tortoise because there are infinite numbers of time series in the sum, We modern people will laugh at them because the sum of infinite numbers is limited to "2".
My story, is totally different, from 1st to 20th seconds, a 45 degree diving a/c acceleration changes from g(usually higher) to 0. During the dive process, a/c moves to equilibium point. The acceleration is always decreasing. If you treat it as a constant acceleration motion, you'll make a mistake.