Neighbor's electricity cable (digging to find cable, hook up to it)

T

Trex123

New member
Joined
Apr 8, 2023
Messages
2
Please help with my homework.

The neighbor's electricity cable runs straight through our square plot of land with the sides of 1. We would like to find the cable
and connect to it, but unfortunately we don't know where exactly this cable goes. Find a way to dig up
the garden so that we are guaranteed to find the cable for all configurations.
In the lecture, we showed that if we dig all sides of the square, the length of the excavation will be 4.
Furthermore, we figured, that there is no need to dig up all 4 sides, but to dig up only three sides and thereby obtain
solution of 3. The variant with digging both diagonals of the plot had a solution of 2√2. Your job is to find it
solution of xddddddddddd.PNG Don't forget to show the procedure for calculating the exact way to dig.

Thank you.
 
Trex123 said:
Please help with my homework.

The neighbor's electricity cable runs straight through our square plot of land with the sides of 1. We would like to find the cable
and connect to it, but unfortunately we don't know where exactly this cable goes. Find a way to dig up
the garden so that we are guaranteed to find the cable for all configurations.
In the lecture, we showed that if we dig all sides of the square, the length of the excavation will be 4.
Furthermore, we figured, that there is no need to dig up all 4 sides, but to dig up only three sides and thereby obtain
solution of 3. The variant with digging both diagonals of the plot had a solution of 2√2. Your job is to find it
solution of View attachment 35498 Don't forget to show the procedure for calculating the exact way to dig.

Thank you.
Click to expand...
Is this a school HW or practical problem?
 
Trex123 said:
Please help with my homework.
Don't forget to show the procedure for calculating the exact way to dig.
Click to expand...
This is a math help site which means we help students solve their homework problem. Do you really think that if one of the helpers here solved your problem that would be helpful to you?

Please read the forum's posting guidelines and make a new post following the guidelines.
 
Trex123 said:
Please help with my homework.

The neighbor's electricity cable runs straight through our square plot of land with the sides of 1. We would like to find the cable
and connect to it, but unfortunately we don't know where exactly this cable goes. Find a way to dig up
the garden so that we are guaranteed to find the cable for all configurations.
In the lecture, we showed that if we dig all sides of the square, the length of the excavation will be 4.
Furthermore, we figured, that there is no need to dig up all 4 sides, but to dig up only three sides and thereby obtain
solution of 3. The variant with digging both diagonals of the plot had a solution of 2√2. Your job is to find it
solution of View attachment 35498 Don't forget to show the procedure for calculating the exact way to dig.

Thank you.
Click to expand...
In order to help, we need to see where you need help; you'll need to have done some thinking of your own.

If you've done no thinking at all, you'll at least need to show us exactly what was done in the lecture, and tell us what topics you are learning, so we can see what you are expected to learn from this exercise. How good are your notes?

Now, I can see where they get their number, and how to prove it by modifying what was already done; but in fact, there is a lower number you could get, if you knew calculus (or how soap bubbles work). It appears, therefore, that you are not expected to find the actual minimum, but to work backward from their number. This confirms that we need to see what you have been taught, so we can help you use that.
 
Trex123 said:
Please help with my homework.

The neighbor's electricity cable runs straight through our square plot of land with the sides of 1. We would like to find the cable
and connect to it, but unfortunately we don't know where exactly this cable goes. Find a way to dig up
the garden so that we are guaranteed to find the cable for all configurations.
In the lecture, we showed that if we dig all sides of the square, the length of the excavation will be 4.
Furthermore, we figured, that there is no need to dig up all 4 sides, but to dig up only three sides and thereby obtain
solution of 3. The variant with digging both diagonals of the plot had a solution of 2√2. Your job is to find it
solution of View attachment 35498 Don't forget to show the procedure for calculating the exact way to dig.

Thank you.
Click to expand...
khansaheb said:
Is this a school HW or practical problem?
Click to expand...
 
Hello, thanks for your replies and sorry for the wrong aproach. I managed to solve the exercise by drawing a lot of different options of lines in a square in a drawing programme. Here is my result: efg.PNG

Do you think you could explain to me how you get the number to go even lower?
 
As a practicing research engineer, I had brought many "practical" problems home - that needed different attacking angle.
 
A hint: start with the diagonals and tweak it to decrease the total length. This way I got a solution with the total length of [imath]1+\sqrt{3}[/imath], which is slightly less than [imath]\frac{1}{2}+\sqrt{5}[/imath], but the solution can easily be modified to get the required length.

think of the diagonals as a 1D version of soap bubbles.
 
Trex123 said:
Hello, thanks for your replies and sorry for the wrong aproach. I managed to solve the exercise by drawing a lot of different options of lines in a square in a drawing programme. Here is my result: View attachment 35500

Do you think you could explain to me how you get the number to go even lower?
Click to expand...
That gives 2 + sqrt(2)/2 = 2.707...; the goal they set is 1/2 + sqrt(5) = 2.736...; what @blamocur and I both got is 1 + sqrt(3) = 2.732..., a little lower than theirs, but not as low as yours. Since they actually asked for something less than their goal, you have a valid solution, and one that is better than ours. Good work! I don't know of anything lower.
 
Dr.Peterson said:
...but in fact, there is a lower number you could get, if you knew calculus (or how soap bubbles work).
Click to expand...
Ooops, I've noticed this part of your post only now, after I've mostly duplicated it in my post.
 
blamocur said:
As @Dr.Peterson mentioned, my solution is inferior to yours, but since it is a legitimate solution, here it is:
View attachment 35504
Click to expand...
Their number comes from the same arrangement, but with the horizontal segment being a different length. The [imath]\sqrt{5}[/imath] hints at how to find it: the slanted segments have a slope of 2:1, so their length involves [imath]\sqrt{5}[/imath].

The optimal solution of this configuration has 120 degree angles (the soap bubble angle).

I'm not sure how you would try to prove the minimal length over all possible configurations that meet the requirement.
 
You must log in or register to reply here.
Top