A large space agency has decided to build a base on the moon. For this purpose, a cable must be laid around the moon's equator. When the cable is laid, it turns out to be 1 meter short. In a quickly arranged meeting, it is decided to investigate the possibility to lay the whole cable in a groove.
How deep does the groove need to be to make this work?
The agency's director considers digging a groove, no matter how deep, around the entire circumference is too expensive. He suggests to lay the whole cable just a bit north of the equator. How many meters north of the moon's equator should the cable be laid to settle the problem of the lacking 1 meter of cable?
I'm posting one puzzle, riddle, math, or statistical problem a day. Try to answer each one and post your answers in the comments section. I'll post the answer the next day. Even if you have the same answer as someone else, feel free to put up your answer, too!
Tuesday, June 21, 2011
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Is it 7/44th of a metre.ReplyDelete
The groove needs to be 0.16 m deep. Since it's to expensive to dig such a long groove the cable should be laid 42616 meters north or south of the equator.ReplyDelete
The circumference of a circle is 2πr. To make the circumference a meter shorter, subtract one: 2πr - 1. To get the circumference formula again, subtract 1 in the form of 2π/2π and factor out a 2π to get 2π(r - 1/2π). The trench has to be 1/2π m (about 0.16 m or half a foot) deep.ReplyDelete
To find out how far north to move, construct a right triangle with hypotenuse r, long leg r - 1/2π, and short leg y, the amount north to move. Appeal to Pythagoras' theorem to find that y is √(r/π - (1/2π)²). The moon's radius is about 1700 km, a third of that is about 600, and the square root of that is about 24 m, about 79 feet.