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A string is drawn between two 10 meter tall poles.

At its lowest point, the string is 3 meters off the ground.

The total length of the string is 14 meters.

What's the distance between the two poles?

amWhy
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Itamaram
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1 Answers1

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Draw a picture. The string has to travel $10-3=7$ metres downwards, and also $7$ metres upwards. But the string is only $14$ metres long, so the poles must be touching.

André Nicolas
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  • Maybe that there is another solution if the ground is not horizontal? – Emilio Novati Jul 13 '16 at 14:35
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    @EmilioNovati: without further information, we must assume the ground is flat and straight between the bases of the poles. Yes, if there is a hill in the middle the poles can be a ways apart, but then we cannot solve the problem. – Ross Millikan Jul 13 '16 at 14:40
  • I feel pretty silly now. I've found this question yesterday with no context, so I've assumed it came from a calculus textbook. I've modeled the curve in various ways, and battled integrals I haven't seen in years in order to compute this, but repeatedly got "nonsensical" infinitesimally small answers, which were "obviously" wrong. Should've had a second look... – Itamaram Jul 13 '16 at 22:14
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    @Itamaram: It is in some ways a good question. It is tempting, when one sees a question, to attack it with heavy machinery. Many questions, particularly when one is consulting, yield to quite basic tools. – André Nicolas Jul 13 '16 at 22:22