The extra metre of rope, lifted at one point
A rope is stretched tightly around the Earth's equator (radius about 6,371 km). You cut it, splice in one extra metre, and the rope is now slightly slack.
The well-known version raises the rope evenly all the way round: the gap is only about 16 cm. This version is different. Grab the rope at one point and pull it straight up, keeping it taut, so that it lies flat on the ground everywhere except near your hands, where it rises in two straight lines to the lifted point. How high can you lift it?
Guess first. Most people guess a few centimetres.
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The two straight parts of the rope are tangents to the Earth from the lifted point. Write the total length of the lifted rope in terms of the angle between the point of contact and the point directly below your hands, and compare with the length of the ground it no longer covers.
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