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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.....
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Originally posted by ranjan sinhaWill it be T = D / ( V - U ) ?
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.....
Originally posted by ranjan sinhaLet L = distance between the cat and the mouse.
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.....
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.
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Originally posted by ranjan sinhaI have worked it out . My method is a bit lengthy. If my method is not wrong then:-
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.....
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).
Originally posted by CoolPlayerGive the steps of your calculation...don't be weasel-like..
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).
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Originally posted by CoolPlayerI looked up Irodov.
See problem no. 1.13 of I.E.Irodov's "Problems in General Physics"..
In the answer section the basic steps have been given.
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.
Originally posted by howzzatIrodov is an established authority in the world of academia.
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.
Be double-ly triple-ly sure before pointing fingers at such authorities on the subject..