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Philosophy, Metaphysics & the Afterlife
Infinity:The headstart paradox
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<blockquote data-quote="mr_bumpkin" data-source="post: 24500" data-attributes="member: 513"><p><strong>Re: Infinity:The headstart paradox</strong></p><p></p><p>we'll say man B runs at a constant 10 m sec now.</p><p> </p><p>Man A waits till man be has gone 30 m (so he waits three seconds)</p><p> </p><p>Second #4 </p><p>ManA takes off at 20 m second, for a total of 20 m traveled.</p><p>ManB continues at 10m second, for a total of 40 m traveled.</p><p> </p><p>Second # 5 and #6</p><p>Man A drops his speed to 12.5 m sec, so by the end of second #6 he's gone 45 m</p><p>Man B continues at 10 m sec, so by the end of second #6 he's gone 60 m</p><p> </p><p>Second # 7 and # 8</p><p>Man A continues at 12.5 m sec, so by the end of second #8 he's gone 70 m.</p><p>Man B continues at 10 m sec, so by the end of second #8 he's gone 80 m.</p><p> </p><p>Second #9 and #10</p><p>Man A drops his speed to 11.875 m sec, so by the end of second #10 he's gone 93.75 m</p><p>Man B continues at 10 m sec, so by the end of second #10 he's gone 100 m.</p><p> </p><p>Second #11 and # 12</p><p>Man A drops his speed further to 11.25 m sec, so by the end of second #12 he's gone 116.25 m.</p><p>Man B continues at 10 m sec, so by the end of second #12 he's gone 120 m.</p><p> </p><p> </p><p>See where this is going (I actually needed a calculator for that last one)? If the distance between the runners is really to diminish by half every round of running, Man A's speed must steadily be approaching that of Man B, getting slower and slower until they're running almost-but-not-quite the same speed.</p><p> </p><p>If such a condition could be reached, then man A would never pass man B, though he would get close enough to tap him on the shoulder, and the race would be a real precision photo finish, of course.</p><p> </p><p>But.... that's quite a condition.</p></blockquote><p></p>
[QUOTE="mr_bumpkin, post: 24500, member: 513"] [b]Re: Infinity:The headstart paradox[/b] we'll say man B runs at a constant 10 m sec now. Man A waits till man be has gone 30 m (so he waits three seconds) Second #4 ManA takes off at 20 m second, for a total of 20 m traveled. ManB continues at 10m second, for a total of 40 m traveled. Second # 5 and #6 Man A drops his speed to 12.5 m sec, so by the end of second #6 he's gone 45 m Man B continues at 10 m sec, so by the end of second #6 he's gone 60 m Second # 7 and # 8 Man A continues at 12.5 m sec, so by the end of second #8 he's gone 70 m. Man B continues at 10 m sec, so by the end of second #8 he's gone 80 m. Second #9 and #10 Man A drops his speed to 11.875 m sec, so by the end of second #10 he's gone 93.75 m Man B continues at 10 m sec, so by the end of second #10 he's gone 100 m. Second #11 and # 12 Man A drops his speed further to 11.25 m sec, so by the end of second #12 he's gone 116.25 m. Man B continues at 10 m sec, so by the end of second #12 he's gone 120 m. See where this is going (I actually needed a calculator for that last one)? If the distance between the runners is really to diminish by half every round of running, Man A's speed must steadily be approaching that of Man B, getting slower and slower until they're running almost-but-not-quite the same speed. If such a condition could be reached, then man A would never pass man B, though he would get close enough to tap him on the shoulder, and the race would be a real precision photo finish, of course. But.... that's quite a condition. [/QUOTE]
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