How much slack will result if we make the equator ten feet longer?
The equator of the earth is 25,000 miles long (for the sake of this problem). We can consider it as a rope around a sphere. Take the rope off, make it ten feet longer, and put it back in place exactly where it originally was. It will be a little loose (i.e. it will have some slack). Adjust the elongated rope so that the slack is equidistant all along the equator.
How many inches would that slack measure?
The answer is 19.
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1 solution
To find the slack, we need to find the difference between the earth's original radius and the one formed with the slightly longer circumference from the elongated rope. The problem is easily solved by solving for R2-R1, where R1 is the original radius and R 2 is the longer one. Using R = C/2Pi we get R2-R1 = (C2-C1)/2Pi. Or, R2-R1= (25,000 miles +10 feet -25,000 miles)/6.3 = 10 feet/6.3 = 1.59 feet= 19 inches.
The non-intuitive observation from this solution is that the answer is independent of the original circumferecne.