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Where on Earth II (Posted on 2005-01-16) Difficulty: 3 of 5
Is it possible to determine the location of an object, if:-

The date is 21st July
The object is 5 Metres tall
The Shadow at 9AM GMT is 31.75 metres long,
The Shadow at Noon GMT is 6.22 metres long,
The Shadow at 3PM GMT is 2.68 metres long.

(On 21 July, the sun is 20.4 north of the equator and crosses the meridian 6.3 minutes after local noon.)

No Solution Yet Submitted by Juggler    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Hints/Tips Clues | Comment 2 of 4 |

The sun is so far away from the earth that its rays can be considered parallel.  In fact, the major lack of parallelism is the sun's diameter, rather than its proximity to earth (after all, it's much bigger than the earth).

So, if the sun is at a given height in the sky (measured in degrees), that determines a circle of a certain radius around the point where the sun is directly overhead. All along this circle, the sun is the same height in the sky.

Two such readings give two circles, that intersect, in general, in two points.

So the third reading can select which of the two is correct.

  Posted by Charlie on 2005-01-16 21:44:40
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