一只鳄鱼与一个人的故事

题意

在一个有一个圆形岛屿，半径为 $1$，有一个人在岛屿的正中央。一只鳄鱼在岛屿的一个边境上。鳄鱼每时每刻都想更靠近这个人一点，如果已经最近了就停下不动。问这个人如何逃离这个岛屿。鳄鱼的移动速度是人的 $4$ 倍。

题解

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在以岛屿中心为中心的，半径为 $\frac14$ 的小圆里，人有速度优势，就是绕圆心转 $360$ 度的速度比鳄鱼快。所以我们可以利用这个速度优势，转到鳄鱼，圆心，人这三点在一条直线上。然后直接逃离这个岛。

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Problem Statement

There is a circular island with radius $1$, and a person is standing at the center of the island. A crocodile is at the boundary of the island. The crocodile always wants to get closer to the person, and will stop moving if it has already reached the closest position. How can the person escape from the island? The crocodile's movement speed is $4$ times that of the person.

Solution

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The person has a speed advantage within a small circle centered at the island's center with radius $\frac14$. The speed of the person around the center is faster than the crocodile. Therefore, we can use this speed advantage to move to the crocodile, the center of the island, and the person, so that they are all on the same line. Then we can directly escape from the island.

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• 分类： 做题笔记
• 最后更新于：2023-02-25 11:59:15^UTC+8
• 标签： 思维