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Problem involving ratios to find the length of a shadow

by overhorizon
Tags: involving, length, ratios, shadow
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overhorizon
#1
Aug26-10, 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 1-to-8 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.
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presbyope
#2
Aug27-10, 04:38 PM
PF Gold
P: 44
Quote Quote by overhorizon View Post
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 1-to-8 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.
You forgot to tell us what Syene has to do with the problem. Is there a shadow there? But yes, on a smaller planet Alexandria would be closer to the equator and would have a smaller shadow.

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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