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My professor has given me an extremely hard physics problem I need the solution to.

Basically the problem is as follows:a cat is sitting in the bottom left corner of a room with sides length a,while a mouse is sitting in the bottom right corner with the mouse hole being in the top right corner.

The velocity of the mouse is V,and the velocity of the cat is 2V.

The velocity of the mouse is always headed towards the hole,while the cat's velocity is always headed towards the mouse.

You need to find the distance the mouse will cover before the cat catches it.

The answer is (2/3)a , with a being the lenght of the sides of the square room.

How do you solve this without integrals or any complex maths?

I would really appreciate it.

Filip Golubovic
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    Does this answer your question? https://en.wikipedia.org/wiki/Radiodrome – Daniel Schepler Nov 12 '21 at 23:21
  • So the room is a square? And what does "How do you solve this without integrals or any complex maths?" mean? – Paul Frost Nov 12 '21 at 23:29
  • @PaulFrost It means that if you posed the question to a high school pre-calculus student, who was familiar with Geometry, Algebra, and Analytical Geometry, and you had crafted an elegant answer that the student could understand, what would that answer be? – user2661923 Nov 13 '21 at 00:05
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    See for example, Cat Dog problem using integration though I don't think it can be solved without at least some calculus. – dxiv Nov 13 '21 at 00:09
  • @DanielSchepler The linked article is certainly on point. Unfortunately, it violates the OP's (i.e. original poster's) simplicity constraint. See, for example my previous comment. To The OP: What leads you to believe that, re my previous comment, there is such a simple elegant solution? – user2661923 Nov 13 '21 at 00:10
  • @user2661923 How can you be sure that the OP is a high school pre-calculus student? Perhaps his professor claimed that there is an "elementary" solution? – Paul Frost Nov 13 '21 at 00:10
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    @PaulFrost "How do you solve this without integrals or any complex maths?" I can only take that one way. – user2661923 Nov 13 '21 at 00:12
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    @user2661923 The OP should clarify it. – Paul Frost Nov 13 '21 at 00:16
  • @PaulFrost Hypothetically, if you were a pre-calculus student, would you be able to clarify what math should not be used? That is asking a little too much of a math student, who doesn't know what he doesn't know. – user2661923 Nov 13 '21 at 00:18
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    To the OP: The easy way out of the issue of what math you wish to have considered off limits is by very carefully stating your math background. This will inform mathSE reviewers what boundaries of knowledge need to be considered. – user2661923 Nov 13 '21 at 00:20
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    @user2661923 I went one step further: I know that I know nothing. – Paul Frost Nov 13 '21 at 00:26
  • I voted to close your question because the discussion in the comments did not evoke any reaction. – Paul Frost Nov 19 '21 at 22:46
  • An interesting problem. As mentioned above the complete solution is here https://math.stackexchange.com/questions/244333/cat-dog-problem-using-integration. Another question is what is the smallest cat's velocity, which ensures that the mouse is caught, i.e. exactly at the hole entrance. The solution from the link above yields approximately $1.618v$. – Vítězslav Štembera Dec 02 '21 at 09:44

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