When will the cat catch the mouse? ranjan sinha Posers and Puzzles 05 Jul '06 14:34
1. 05 Jul '06 14:341 edit
At the start, a mouse is at a distance 'D' to the north of a cat. The mouse starts running with a constant speed 'U' towards east. The cat starts running with a constant speed 'V' always directed towards the mouse. ( V > U ). Obviously the cat will catch the mouse in a finite time. Find an analytical expression for the time T required for the cat to catch the mouse in terms of U , V and D. The differential equation you will need may involve second order derivatives..... 😲🙄🙄
Some guys say this is an unsolvable problem. But it has been analytically solved by.....
2. 06 Jul '06 10:421 edit
Originally posted by ranjan sinha
At the start, a mouse is at a distance 'D' to the north of a cat. The mouse starts running with a constant speed 'U' towards east. The cat starts running with a constant speed 'V' always directed towards the mouse. ( V > U ). Obviously the cat will catch the mouse in a finite time. Find an analytical expression for the t ...[text shortened]... say this is an unsolvable problem. But it has been analytically solved by.....
Will it be T = D / ( V - U ) ?
3. 06 Jul '06 14:22
If you just want the answer in YES or NO , then it is YES.
4. 06 Jul '06 14:26
Originally posted by sarathian
Will it be T = D / ( V - U ) ?
No.
5. 06 Jul '06 14:33
i withdraw my suggested answer. I wrongly assumed the cat and mouse
both running in the same straight line. Sorry. The trajectory of the cat's path will be a complicated curve.. Palynka is right.
6. 06 Jul '06 14:35
Originally posted by Palynka
No.
Correct.
7. 06 Jul '06 14:58
Originally posted by sarathian
Will it be T = D / ( V - U ) ?
You are outrageously wrong... Simple arithmetic won't do. It involves calculus..
8. 07 Jul '06 09:59
Originally posted by ranjan sinha
At the start, a mouse is at a distance 'D' to the north of a cat. The mouse starts running with a constant speed 'U' towards east. The cat starts running with a constant speed 'V' always directed towards the mouse. ( V > U ). Obviously the cat will catch the mouse in a finite time. Find an analytical expression for the t ...[text shortened]... say this is an unsolvable problem. But it has been analytically solved by.....
Let L = distance between the cat and the mouse.
S = distance traversed by the cat.
Then S = V * T. If one could set up an expression for the
derivative dL/dS , or dL/dT, the problem can be solved.
At T = 0, S= 0 and L = D. Therefore the time T at which L = 0 will be the required solution. But I am not abe to set up the differential equation between L and S exclusive of other variables. Other variables appear intermingled and I don't know how to eliminate the other variables using the conditions of the problem. I am trying..
When something comes up I will be back.
9. 07 Jul '06 12:522 edits
Originally posted by ranjan sinha
At the start, a mouse is at a distance 'D' to the north of a cat. The mouse starts running with a constant speed 'U' towards east. The cat starts running with a constant speed 'V' always directed towards the mouse. ( V > U ). Obviously the cat will catch the mouse in a finite time. Find an analytical expression for the t ...[text shortened]... say this is an unsolvable problem. But it has been analytically solved by.....
I have worked it out . My method is a bit lengthy. If my method is not wrong then:-
The time taken by the cat to catch the mouse will be
T = ( V * D ) / (V^2 - U^2).
The distance S covered by the cat in cathing the mouse will be
S = (V^2)*D /(V^2 - U^2).
10. 07 Jul '06 14:16
Originally posted by CoolPlayer
I have worked it out . My method is a bit lengthy. If my method is not wrong then:-
The time taken by the cat to catch the mouse will be
T = ( V * D ) / (V^2 - U^2).
The distance S covered by the cat in cathing the mouse will be
S = (V^2)*D /(V^2 - U^2).
Give the steps of your calculation...don't be weasel-like..
11. 07 Jul '06 15:18
See problem no. 1.13 of I.E.Irodov's "Problems in General Physics"..
In the answer section the basic steps have been given.
12. 07 Jul '06 15:39
Originally posted by CoolPlayer
See problem no. 1.13 of I.E.Irodov's "Problems in General Physics"..
In the answer section the basic steps have been given.
oh yes i have a copy of that handy i'll go look it up.😠
13. 07 Jul '06 16:332 edits
Originally posted by CoolPlayer
See problem no. 1.13 of I.E.Irodov's "Problems in General Physics"..
In the answer section the basic steps have been given.
I looked up Irodov.
Irodov seems to be wrong. Irodov has taken the instantaneous velocity of approach ( he has used 'convergence'😉 to be

( V - U cos a ),
where 'a ' is the instantaneous angle between the directions of motion of the cat and the mouse.
But the the instantaneous velocity of approach must be the instantaneous relative velocity of the cat w.r.t. the mouse.
It should accordingly be

SQRT (V^2 - 2 U V cos a + U^2).

Irodov seems to be wrong.
Either Irodov must be wrong or we have a contradiction.
14. 07 Jul '06 17:33
Originally posted by howzzat
I looked up Irodov.
Irodov seems to be wrong. Irodov has taken the instantaneous velocity of approach ( he has used 'convergence'😉 to be

( V - U cos a ),
where 'a ' is the instantaneous angle between the directions of motion of the cat and the mouse.
But the the instantaneous velocity of approach must be ...[text shortened]... v seems to be wrong.
Either Irodov must be wrong or we have a contradiction.
Irodov is an established authority in the world of academia.

Be double-ly triple-ly sure before pointing fingers at such authorities on the subject..
15. 07 Jul '06 17:591 edit
Originally posted by ranjan sinha
Some guys say this is an unsolvable problem. But it has been analytically solved by.....
Alan Curry --> http://mathproblems.info/group2.html (see problem #30)
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