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Train Station (Posted on 2007-02-11) Difficulty: 3 of 5
A local person was about to get into the last car of a train when the door closed and the train started moving with a constant acceleration of 1.0476 m/sē. However, the door of the next car 50 m away was still open so he ran and got into the train.

Where is this train station located?

No Solution Yet Submitted by Art M    
Rating: 2.0000 (2 votes)

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Solution The presumably intended solution (spoiler). | Comment 2 of 5 |

After t seconds the train will have moved .5238 t^2 meters. The sprinter will have had to travel 50 meters more than this.

Given a needed distance to travel, we can find the time necessary by

t = sqrt((dist-50)/.5238)

Tabulating the possible distances, times and speeds:

meters   sec    m/s
 60.00   4.37  13.73
 70.00   6.18  11.33
 80.00   7.57  10.57
 90.00   8.74  10.30
100.00   9.77  10.24
110.00  10.70  10.28
120.00  11.56  10.38
130.00  12.36  10.52
140.00  13.11  10.68
150.00  13.82  10.86
160.00  14.49  11.04
170.00  15.14  11.23
180.00  15.75  11.43
190.00  16.35  11.62
200.00  16.92  11.82

The least speed needed by the sprinter, 10.24 m/s, happens to be for 100 meters at the world record time for the 100-meter run, held by Asafa Powell of Jamaica, but also claimed by Justin Gatlin of the United States.

Presumably the intended answer is the island of Jamaica, but it's probable that Gatlin could also make that time, and he is a native of the U.S.

The possibility of this accomplishment is dependent on the runner being in best form, ready for a race, which is an unlikely situation even for an olympic runner while casually trying to catch a train (especially if he has any luggage--even a briefcase).

  Posted by Charlie on 2007-02-11 13:07:00
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