The Other Rope Around The Earth Solution

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• The Other Rope Around the Earth

The rope stretches from the top of the pole to the horizon. Suppose the angle subtended by the rope is t, the radius of the Earth is R, and the distance to the horizon is D. Then

• (1) D^2+R^2 = (R+h)^2
• (2) D = R.tan(t)
• (3) R.t + 3 = D.

• (4) tan(t) ~ t + t^3/3

• (5) R.t + 3 = R.tan(t) [ from (2) and (3) ]
• (6) t + 3/R ~ t + t^3/3 [ from (5) and (4) ]
• (7) t^3 ~ 9/R [ rearranging (6) ]

(drum roll please ...)

h ~ 401 metres.

• The Other Rope Around the Earth
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