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Question:
A cable, 16 meters in length, hangs between two pillars that are both 15 meters high. The ends of the cable are attached to the tops of the pillars. At its lowest point, the cable hangs 7 meters above the ground. How far are the two pillars apart?

Question

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Question: 	
A cable, 16 meters in length, hangs between two pillars that are both 15 meters high. The ends of the cable are attached to the tops of the pillars. At its lowest point, the cable hangs 7 meters above the ground. How far are the two pillars apart?

tkhunny · Answer

I suppose we are to assume the cable is perfectly flexible and of uniform density.

Do you know the actual model for such a hanging cable?  It isn't a parabola.

baseballer2014 · Answer

we do not have the model but just think about the pillars and the cable is flexible

tkhunny · Answer

"we do not have the model" - That is false.

For what course have you been given this problem?

baseballer2014 · Answer

AP calculus but this was a leisure time activity our teacher gave us, he told us to ponder it for the night and i have drawn no solution

tkhunny · Answer

Have you met the hyperbolic cosine?

baseballer2014 · Answer

it doesn't seem to take the shape of any function I've already tried that but the one hint our teacher gave us was that it is easier than it appears and to use logic

tkhunny · Answer

Fair enough.  If we stretch the cable tight, the poles are obviously 16 m apart.  If there is any bend at all, they will be closet than 16 m.  Make sense?

baseballer2014 · Answer

absolutely but then that draws the question, how far apart do the need to be to make the cable only hang 7ft

tkhunny · Answer

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What do you think of this drawing?