Does Distance Decrease between you and an object as your elevation increases?

[kingofjong]

Hello

I was wondering if I put a box on the ground and then walk 100 yards away, the distance between the box and me is 100 yards. At 100 yards if I clime a tree will the distance between me and the box decrease as elevation increases? If yes then by how much will it decrease if I am elevated 50 yards from the ground?

Thank you

[studiot]

2 minutes ago, kingofjong said:

Hello

I was wondering if I put a box on the ground and then walk 100 yards away, the distance between the box and me is 100 yards. At 100 yards if I clime a tree will the distance between me and the box decrease as elevation increases? If yes then by how much will it decrease if I am elevated 50 yards from the ground?

Thank you

No the distance increase very slightly as you are further from the centre of the earth.

But this is the physical or actual distance your would measure with a tape measure.

For this reason all map distances are calculated at a standard ditance from the centre of the Earth  -  Sea level is normally used.

So if you were 50 yards above sea level and measured 100 yards to another object, also 50 yards above sea level you would say that your reduced distance (reduced to sea level) is just under 100yards.

The difference is not significant below an elevation of about 1000 feet above sea level, unless you are doing some very advanced surveying.

[Country Boy]

Where in theworld did you get the idea that that the distance would decrease?

The tree is perpendicular to the ground so you have a right triangle.  Your view-line from yourself, up the tree, and the object is the hypotenuse of a right triangle. The hypotenuse is always longer than the other two sides, not shorter!

[studiot]

3 minutes ago, Country Boy said:

Where in theworld did you get the idea that that the distance would decrease?

The tree is perpendicular to the ground so you have a right triangle.  Your view-line from yourself, up the tree, and the object is the hypotenuse of a right triangle. The hypotenuse is always longer than the other two sides, not shorter!

Sadly the king of jong only stopped by long enough to make his post, but has been to busy with his subjects to come back to us peasants, but +1 for an excellent comment.

[swansont]

1 minute ago, studiot said:

+1 for an excellent comment.

I’m not sure I’d include “berating someone for not knowing something” in that assessment.

 

[Phi for All]

2 hours ago, Country Boy said:

Where in theworld did you get the idea that that the distance would decrease?

2 hours ago, studiot said:

Sadly the king of jong only stopped by long enough to make his post, but has been to busy with his subjects

Some version of Skitt's Law will get you if you misplay the ridicule card. If the box on the ground is full of stones, and the tree is next to a glass house....

[Country Boy]

I have no problem with a person not knowing something.   I do have a problem with a person asserting something that is not true!

[swansont]

55 minutes ago, Country Boy said:

I have no problem with a person not knowing something.   I do have a problem with a person asserting something that is not true!

OK, but that didn’t happen here. They asked if something was true, and if so, how big the effect would be. Did you misread the OP?

[Ghideon]

Maybe @kingofjong can clarify if this is more of a "trick question" where the shape of the tree makes difference. Something like this, where position A and B has same elevation but not same distance to the box "X"

 

(I note that "50 yards of the ground" may rules out "A" above if the size of the tree is to be realistic) 

 

[MigL]

I would assume he meant the difference between the aarc-length ( the Earth being round ), and the straight line distance to the top of the tree ( or 50 yards height ).
In that case, at the distances being considered ( 100 yards ), the arc length is essentially equal to a straiight line, so the straight line distance to the top of the 50 yard tree is longer than the arc length to the base, or approximately  (100²+50²)^1/2.

Edited July 16, 2021 by MigL

[A_curious_Homosapien]

On 7/17/2021 at 12:43 AM, Country Boy said:

I have no problem with a person not knowing something.   I do have a problem with a person asserting something that is not true!

You sounded like a dad trying to teach his 10 year old son mathematics. Lol

On 7/17/2021 at 1:46 AM, Ghideon said:

Maybe @kingofjong can clarify if this is more of a "trick question" where the shape of the tree makes difference. Something like this, where position A and B has same elevation but not same distance to the box "X"

 

(I note that "50 yards of the ground" may rules out "A" above if the size of the tree is to be realistic) 

 

Well in that way we can draw a perpendicular from from A and the Root of the Tree in such a way that we get 2 right triangles sharing the same hypotenuse. Then by some pythagorean tricks and some trigonometry find the answer.

[mistermack]

If kingofjong wants to picture why the distance increases, he would be better off picturing the box being one yard away from the tree, rather than 100 yards. It's then obvious, if you climb 50 yards up the tree, you will be much further away from the box.