The Oil Problem
An oil well being drilled in flat prairie country struck pay sand at an under ground spot exactly 21,000 feet from one corner of a rectangular plot of farmland, 18,000 feet from the opposite corner, and 6000 feet from a third corner.
How far is the underground spot from the fourth corner ?
How far is the underground spot from the fourth corner ?
Labels: logic, mathemagic
posted by ToM at
8:39 PM
11 Comments:
my name is potter and i left the first comment. i shall conquer the world!!!
3000 ft below the surface, i think.
by the way, what should i expect to find at the end of the universe?
It's 27,000 feet from the 4th corner.
The geometry is hard to explain, so bear with me.
First I tried constructing a rectagular pyramid with an off-center point, but the geometry got a little complicated. So I simplified it by constructing a rectangle with an off-center point inside it, and drew lines from the point to each corner. Then I drew lines from the point perpedicular to each edge, so that I had 4 rectagles each with a line bisecting it into 2 equal right-triangles. Then I just used trig to solve for the missing length, using unknown varaibles for the dimensions of the plot. All the unknown varaibles cancelled each other out, revealing the missing dimension.
Since the dimensions of the plot are arbitrary, the depth of the spot is also arbitrary but related. But if you defined the dimensions of the plot, you could probably solve for the depth using a pyramid.
Someone else can probably explain the geometry better than I can, and there's probably an easier way to solve it, but yeah, it's 27,000 feet.
You explained it well, thank you (ha ha..."well"). Seriously though, I understood it.
I also understand that domestic oil drilling will NOT solve, or even really help, our economic and energy crisis. There are already millions of acres of oil fields that the oil companies are allowed to drill on but are not. They only want permission to drill on more lands to affect the speculators'/investors' prices, so that in the end they can get more profit. They have fooled the public into thinking that we have all this oil at home that we can safely get and it then gas will be a dollar again. So the mindless masses chant "Drill, Baby, Drill" without any regard to the scientific facts.
The facts are that we have 3% of the world's oil, but we use 25% of it. Even if we drill it ALL, disregarding the environment and wildlife (the same disregard that has gotten us into this mess, because if people had chosen to get off fossil fuels 30 years ago when it was proved the damage they did, we would be economically, militarily, and environmentally/public-health wise strong), we would NOT see that oil for 10 years, but because of speculators the prices would drop 1 CENT A GALLON FOR A FEW MONTHS. How is that going to help us? That is putting a band-aid on a bullet-wound.
Life and chemical make-up of the oceans is vital to cleaning our environment and controlling global warming--if we destroy the sea we are in effect ripping out our liver at a time when we are already poisoned. If we allow more off-shore drilling we will be sacrificing the health of the ocean and wildlife, and in turn, our own health and economy, in exchange for a ONE CENT A GALLON, FOR A FEW MONTHS. Destruction forever for a penny now.
Barack Obama does not support more off-shore drilling, but has agreed to reach across the aisle and compromise on some added drilling only if it is part of a comprehensive energy plan that makes us independent of oil in 10 years and reduces are carbon output, helping with the global warming crisis.
So yes, the answer is 27,000 feet, and say no to drilling.
Clarification: we use 25% of the WORLD'S OIL (not our own)--much more than we could ever make at home.
its 40,000. by dividing it into two triangles and using a^2 + b^2 = c^2 the answer can be extrapolated.
---------Hades
t1=21000 ;slope dist from point 1 to (a,b,c); Point (a,b,c) is at well depth
t2=6000 ;point 1 is at (0,0,0) point 2 is at (0,y,0) point 3 is at (x,y,0)
t3=18000 ;point 4 is at (x,0,0)
t1=sqrt(s1^2+c^2)
t2=sqrt(s2^2+c^2)
t3=sqrt(s3^2+c^2)
s1=sqrt(t1^2-c^2) ;surface dist from point 1 to (a,b,0)
s2=sqrt(t2^2-c^2) ;surface dist from point 2 to (a,b,0)
s3=sqrt(t3^2-c^2) ;surface dist from point 1 to (a,b,0)
y=sqrt(s1^2-a^2)+sqrt(s2^2-a^2)
x=sqrt(s2^2-(y-b)^2)+sqrt(s3^2-(y-b)^2)
s1=sqrt(a^2+b^2)
s2=sqrt(a^2+(y-b)^2)
s3=sqrt((x-a)^2+(y-b)^2)
s4=sqrt((x-a)^2+b^2)
t4=sqrt(s4^2+c^2)
y 21593.62281
x 20200.72245
t1 21000
t2 6000
t3 18000
s1 20392.29981
s2 3293.310103
s3 17287.15973
s4 26530.09407
t4 27000
Finally the answer is 27,000
hjg
I omitted a few lines when I pasted.
t1=21000 ;slope dist from point 1 to (a,b,c); Point (a,b,c) is at well depth
t2=6000 ;point 1 is at (0,0,0) point 2 is at (0,y,0) point 3 is at (x,y,0)
t3=18000 ;point 4 is at (x,0,0)
t1=sqrt(s1^2+c^2)
t2=sqrt(s2^2+c^2)
t3=sqrt(s3^2+c^2)
s1=sqrt(t1^2-c^2) ;surface dist from point 1 to (a,b,0)
s2=sqrt(t2^2-c^2) ;surface dist from point 2 to (a,b,0)
s3=sqrt(t3^2-c^2) ;surface dist from point 1 to (a,b,0)
y=sqrt(s1^2-a^2)+sqrt(s2^2-a^2)
x=sqrt(s2^2-(y-b)^2)+sqrt(s3^2-(y-b)^2)
s1=sqrt(a^2+b^2)
s2=sqrt(a^2+(y-b)^2)
s3=sqrt((x-a)^2+(y-b)^2)
s4=sqrt((x-a)^2+b^2)
t4=sqrt(s4^2+c^2)
a 2971.9033
b 20174.5801
c 5015.38718
y 21593.62281
x 20200.72245
t1 21000
t2 6000
t3 18000
s1 20392.29981
s2 3293.310103
s3 17287.15973
s4 26530.09407
t4 27000
hjg
I have refined my meathods and equations, but the answer is still 27,000
Let the Rectangle be x wide and y long
From first corner to oil is t1 (measured along sloping line)
From second corner to oil is t2
From third corner to oil is t3 (third corner is opposite corner from first corner
Find t4, the sloping distance from oil to forth corner.
The oil is found at point (a1,b1,c) where c is the depth to oil
The angle mentioned is from 3rd corner to 2nd corner to point (a1,b1,0)
Ground Distance from a corner to point (a1,b1,0) are s1,s2,s3 and s4
Let c, and the angle be input variables, that you will see have no effect on the
answer for t4.
Equations:
x=a1+a2
y=b1+b2
s1=sqrt(t1^2-c^2)
s2=sqrt(t2^2-c^2)
s3=sqrt(t3^2-c^2)
s4=sqrt(a2^2+b1^2)
t4=sqrt(s4^2+c^2)
s1=sqrt(a1^2+b1^2)
s2=sqrt(a1^2+b2^2)
s3=sqrt(a2^2+b2^2)
a1=cos(angle)*s2
Let angle =60 and c = 2000
Solution:
Input Name Output
21000 t1
6000 t2
18000 t3
t4 27000
x 20033.07766
y 25611.29466
a1 2828.427125
b2 4898.979486
a2 17204.65053
b1 20712.31518
2000 c
s1 20904.54496
s2 5656.854249
s3 17888.54382
s4 26925.82404
60 angle
hjg
PS: making c=0 makes the solution simplier.
but the second corner IS the opposite of the first corner...
I am not even going to bother calculating, but the geology at that depth could be be totally different to the one on top....meaning that the plane may not be flat at all...cheers!
The sum of the squares of the opposite sides of the pyramid equal each other. By reducing the dimensions to 7 and 6, and 2 and 9, we see 49 plus 36 equals 4 plus 81. Makes the problem simple. So 27,000 is the correct answer.
Post a Comment
Links to this post:
Create a Link
<< Home