Imagine a rope wrapped around the Earth at the equator. Then think of adding "d" feet to the rope's length s o it can now circle Earth at a distance "h" feet above the equator at all points.
1. Write an equation to model this situation.
2. Solve your equation for "d"
2. How much rope do you need to insert if you want the rope to circle Earth 500 feet above the eqautor? Use 3.14 for π.
2007-11-01 20:54:49 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Rather easy...
PART 1:
Take the radius of the earth to be R.
So the original rope is:
C = 2 pi R
Now you add 'd' feet to the circumference, which increases the radius by 'h' feet. Here's the equation that models that situation.
C + d = 2 pi (R + h)
PROBLEM 2:
Solve the equation for d by subtracting C from both sides:
d = 2 pi (R + h) - C
Now substitute in the formula above for the original rope length (C):
d = 2 pi (R + h) - 2 pi R
Factor out a common 2 pi:
d = 2 pi (R + h - R)
Cancel out the R values*:
d = 2 pi h
*Notice how the size of the earth doesn't matter in the final equation.
PROBLEM 3:
d = 2 pi h
d = 2 (3.14) 500
d = 1000 x 3.14
d = 3140 ft.
Add 3140 ft. to make it circle the Earth 500 feet above the equator.
2007-11-01 21:08:14 · answer #1 · answered by Puzzling 7 · 0⤊ 0⤋
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2016-10-03 04:06:42 · answer #2 · answered by ? 4 · 0⤊ 0⤋
1)
Radius of earth = h
Length added = d
2)
New radius = h + d
3)
The radius of earth at equator = r = 500 feet
Length of rope = Circumference of earth.
Length of Rope = 2 * TT * r
= 2 * 3.14 * 500
= 3140 feet.
But 1 feet = 0.30 meter
3140 feet = 0.30 * 3140 meters
3140 feet = 942 meters
The length of rope if 3140 feet or 942 meters.
2007-11-01 21:00:13 · answer #3 · answered by Raut N 3 · 0⤊ 1⤋
Circumference=2*radius*π.
Difference between old circumference and new circumference=2*(new radius-old radius)*π.
In this case that'd be:
d=2*h*π
or
h=d/(2*π)
If h is 500, then d=2*500*π= 2*500*3.14=3140.
2007-11-01 21:06:08 · answer #4 · answered by Anonymous · 0⤊ 0⤋
C = 2 pi r
C + d = 2 pi (r + h)
d = [2 pi (r + h)] - C
You do the math.
2007-11-01 21:10:11 · answer #5 · answered by wry humor 5 · 0⤊ 0⤋