Mathematics, 24.10.2020 09:50 kassidyopry15

Imagine a cable fastened snug around the earth along the equator (circumference is about 25,000 miles). Now loosen the cable so that it is 3 feet longer and thus not so perfectly snug anymore. How high off the ground will the cable be?

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Answer from: vickye146

The height of the cable off the ground will be 5.73 inches high.

We are given;

Circumference; C = 25,000 miles

From Conversion tables, we know that;

1 mile = 5280 ft

Thus;

25000 miles = 25000 × 5280

⇒ 132,000,000 ft

We know that formula for circumference is;

C = 2πr

Thus, radius is;

r = C/(2πr)

r = 132,000,000/(2π)

r = 21,008,452.48813 ft

We are told that the cable is loosened so that it is 3 ft longer. This means that the circumference increases by 3 ft.

Thus, $C_{new}$ = 132000003 ft

Let's find the radius of this circumference;

$r_{new}$ = 132000003/(2π)

$r_{new}$ = 21,008,452.965560

To find how high the cable will be off the ground, we will find the difference between the two radius;

Thus;

Height of cable above the ground = $r_{new}$ - r

Height of cable above the ground = 21,008,452.96556 - 21,008,452.48813

Height of cable above the ground = 0.47743 ft

Converting to inches gives us;

Height of cable above the ground ≈ 5.73 inches.

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Imagine a cable fastened snug around the earth along the equator (circumference is about 25,000 mil...

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