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Can the rabbit escape the dog?
Consider a fenced field, 100 meters on a side. There is an open gate at one corner, and a rabbit at the opposite corner. A dumb dog enters the field at the gate, sees the rabbit, and runs directly at it. The dogs runs at 10 m/s. What is the best path for the rabbit to take, to get to the gate? And how fast does the rabbit need to run?
The dog always runs directly at the rabbit. They both run at constant speed.
3 個解答
- ?Lv 72 年前
We had a small beagle, took him hunting.. he found a rabbit and chased it around, around, and down the rabbit hole. We had to yell to him and finally he got turned around and mad it back to the surface. True story.
- 匿名3 年前
No
- billrussell42Lv 73 年前
two possible assumptions:
1. The dog always runs straight at the rabbit no matter where the rabbit is.
2. The dog runs to the rabbit's location and follows the rabbit's path directly.
#1 is most likely, from your wording. But that involves complicated curves as the rabbit heads up one of the sides and the dog's path curves to follow it. At some point the rabbit has to curve towards the gate as the dog curves in behind him. This is very complicated. I have no idea how to solve it, sorry.
