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Problem involving ratios to find the length of a shadow 
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#1
Aug2610, 04:00 PM

P: 1

1. The problem statement, all variables and given/known data
The shadow cast by a vertical pillar in Alexandria at noon during the summer solstice is found to be 1/8 the height of the pillar. The distance between Alexandria and Syene is 1/8 the Earth's radius. Is there a geometric connection between these two 1to8 ratios? I already solved this problem. However, there is another part of the problem: If Earth were smaller than it is, would the shadow of the vertical pillar in Alexandria have been longer or shorter at noon during the summer solstice? 2. Relevant equations Just a ratio I used to solve the first part. Pole shadow/Pole height = Alexandria and Syene distance / Earth radius 3. The attempt at a solution I said the shadow would grow shorter. Since the Earth would be smaller, the distance between Alexandria and Syene would also be smaller. And due to it being a ratio, this would also effect the shadow. However, I am really not certain of my answer and do not know how I could verify it or if I am correct. 


#2
Aug2710, 04:38 PM

PF Gold
P: 44

EDIT: Oops I meant the tropic not the equator. Obviously Syene is on the tropic of cancer south of Alexandria. So there is no shadow there right? 


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