一道有趣的数学题

Suppose you are trying to get from one end A of a terminal to the other end B. (For simplicity, assume the terminal is a one-dimensional line segment.) Some portions of the terminal have moving walkways (in both directions); other portions do not. Your walking speed is a constant v, but while on a walkway, it is boosted by the speed u of the walkway for a net speed of v+u. (Obviously, given a choice, one would only take those walkways that are going in the direction one wishes to travel in.) Your objective is to get from A to B in the shortest time possible.

在机场中,你想从A点前往B点。(为了将问题简化,假设机场是一条线性通道。)一些区域有电动扶梯(双向的),另一些区域没有。你的步行速度恒定为v,电动扶梯的运行速度为u,因此在扶梯上,你的实际速度为v+u。(显然,你不会搭乘与你前进方向不一致的扶梯。)你的目标是尽可能快地从A点到达B点。

1. Suppose you need to pause for some period of time, say to tie your shoe. Is it more efficient to do so while on a walkway, or off the walkway? Assume the period of time required is the same in both cases.

1. 假定你需要暂停片刻,比如系鞋带。请问你应该在电动扶梯上系,还是在没有上电动扶梯时系?假定两种情况下,系鞋带的时间相同。

2. Suppose you have a limited amount of energy available to run and increase your speed to a higher quantity v' (or v'+u, if you are on a walkway). Is it more efficient to run while on a walkway, or off the walkway? Assume that the energy expenditure is the same in both cases.

2. 假定你有有限数量的多余能量,用来奔跑。在跑动时,你的速度提高到v'(如果在电动扶梯上,就相应为v'+u)。请问你应该在电动扶梯上跑,还是在没有上电动扶梯时跑?假定两种情况下,你可供奔跑的能量相同。

3. Do the answers to the above questions change if one takes into account the various effects of special relativity? (This is of course an academic question rather than a practical one. But presumably it should be the time in the airport frame that one wants to minimise, not time in one's personal frame.)

3. 在狭义相对论的情况下,上述答案是否发生改变?

posted on 2018-07-03 13:54  AlanTu  阅读(996)  评论(0编辑  收藏  举报

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