A string is tightly wrapped around the Earth's equator and the two of the string just touch. Now suppose that anoher string is tied to the original string so that it is now 50 feet longer. If this new string is placed around the equator and pulled tight so that it is suspended in air, how high will the string be above the ground.
2007-01-10 12:14:49 · 8 answers · asked by bobo 2 in Science & Mathematics ➔ Mathematics
Well, we know that circumference = 2*pi*radius. And in this case, the circumference is c+50, so we can write that
1. c = 2*pi*r and
2. c+50 = 2*pi*(r+x)
x here is the distance above the ground. Then we can solve the system of equations:
(2*pi*r) + 50 = 2*pi*(r+x)
2*pi*r + 50 = 2*pi*r + 2*pi*x
50 = 2*pi*x
x = 25/pi which is about 7.95774715 feet
Notice how it doesn't matter what r is. So if you do the same thing with an apple, for example, it will still be about 7.95774715 feet.
You could also do this with the formula C=pi*diameter, just remember to divide the answer by two because you only want the height on one side, and not the sum of both sides.
2007-01-10 12:27:36 · answer #1 · answered by Anonymous · 0⤊ 1⤋
I think you are saying that the new string makes a circle around the earth and you want to know how far off the earth the string will be. If this is correct then:
C = 2*pi*r <-- Eq 1
Let x be the amount the string is from the Earth
Then C+50 = 2*pi(r+x) = 2*pi*r +2*pi*x <-- Eq 2
Now subtract Eq 1 from Eq 2 getting:
50 = 2*pi*x
x = 50/2*pi = 7.9577 feet
This answer would be the same if instead of the Earth, you used the Sun or used a dime.
2007-01-10 20:37:58 · answer #2 · answered by ironduke8159 7 · 1⤊ 1⤋
11104.5 feet above the ground.
24,901.55 miles around the equator. Convert to feet which is 131480184 feet. Then add the 50 feet making it 131480234 feet. Put that into the equation for the circumference of a circle Circumference=pi x diameter. With this you find the diameter to be 20925729 feet. The diameter in feet of the Earth is 20903520 feet. The difference is 22209 feet. Divide that by two for each side of the Earth, and you get 1104.5.
2007-01-10 20:35:36 · answer #3 · answered by j_son_06 5 · 0⤊ 2⤋
Lets see... circumference is pi x diamter (C = pi D) for the original string. [ or pi (2r)]
For the lengthened string, the circumference is increased by 50 feet, and the new radius of the circle is increase by the height it is suspended off the ground(h), so for the lengthened string, (C + 50 feet) = pi 2(r + h).
I'll solve for C: C = pi 2(r + h) - 50 feet.
Use the first equation (C = pi 2r), and substitute for C :
pi 2r = pi 2(r + h) - 50 feet
Divide both sides by pi
2r = 2r + 2h - (50 feet / pi)
Rearrange: 2h = 50 feet / pi
(since pi = 3.1415....) h = 25 feet / 3.14159
h = 7.958 feet. The string is suspended 7.958 feet in the air.
2007-01-10 20:28:37 · answer #4 · answered by Anican76 2 · 0⤊ 2⤋
This is so simple, look forget about the equator. 25 feet goes up, 25 feet comes down.
You dont need algebra for that.
2007-01-10 20:23:25 · answer #5 · answered by Anonymous · 0⤊ 2⤋
50 feet
2007-01-10 20:18:57 · answer #6 · answered by ♥♥♥ 3 · 0⤊ 2⤋
25 feet
2007-01-10 20:18:20 · answer #7 · answered by Anonymous · 0⤊ 2⤋
sry i suck at math......
2007-01-10 20:18:40 · answer #8 · answered by lexi(: 3 · 1⤊ 0⤋