When will the cat catch the mouse?

Originally posted by PBE6
Alan Curry --> http://mathproblems.info/group2.html (see problem #30)

Allan Curry's solution and Tristan Simbulan's solutions are rather lengthy. Second order derivatives are involved indeed.

However they give the same result.. as given by Irodov's method.

Surprisingly I.E.Irodov's solution is deceptively simple, elegant and short. It gives the answer in 3 lines without having to do any integration...No differential equation.. no second order derivatives....Only physics ... And lo .... The result appears almost magically from the air...

Originally posted by ranjan sinha
Allan Curry's solution and Tristan Simbulan's solutions are rather lengthy. Second order derivatives are involved indeed.

However they give the same result.. as given by Irodov's method.

Surprisingly I.E.Irodov's solution is deceptively simple, elegant and short. It gives the answer in 3 lines without hav ...[text shortened]... Only physics ... And lo .... The result appears almost magically from the air...

Why don't you talk about your own method?

Originally posted by ranjan sinha
Allan Curry's solution and Tristan Simbulan's solutions are rather lengthy. Second order derivatives are involved indeed.

However they give the same result.. as given by Irodov's method.

Surprisingly I.E.Irodov's solution is deceptively simple, elegant and short. It gives the answer in 3 lines without hav ...[text shortened]... Only physics ... And lo .... The result appears almost magically from the air...

if its only three lines could someone reproduce them here so us non-physicist types could see too. thanks

Originally posted by aginis
if its only three lines could someone reproduce them here so us non-physicist types could see too. thanks

I want to see the three lions too! Are they chasing the cat?

Originally posted by aginis
if its only three lines could someone reproduce them here so us non-physicist types could see too. thanks

Here they are;...Let T be the time required.
Both the cat & the mouse cover the same distanxe X during this time interval along the x-axis assumed to be along east direction. Then

Integral from 0 to T of [V cos a dt]= U*T =X.........Eqn(1)

Where a is the instantaneous angle that cat's velocity makes with X-axis. Obviously a is dependent on the time variable t.


Speed of approach of the cat towards the mouse is V - U cos a. In time T a distance D is covered with this velocity of approach. Hence...

Integral from 0 to T of [(V - U cos a)dt] = D ..........Eqn(2)
From Eqn(1) & (2) we have..
V*T - (U/V)*U T = D ...................................Eqn(3)

This gives at once T = D*V/(V^2 - U^2)
Isn't that cool...No differential equations.. no actual integration..
Only physics and logic.

Originally posted by AThousandYoung
I want to see the three lions too! Are they chasing the cat?

The 3 claimants for the lions-contest are Allen Curry, Tristan Simbulan and Ranjan Sinha
They are still chasing the cat .

Originally posted by ranjan sinha
Here they are;...Let T be the time required.
Both the cat & the mouse cover the same distanxe X during this time interval along the x-axis assumed to be along east direction. Then

Integral from 0 to T of [V cos a dt]= U*T =X.........Eqn(1)

Where a is the instantaneous angle that cat's velocity makes with X-axis. Obviously a is depend ...[text shortened]... that cool...No differential equations.. no actual integration..
Only physics and logic.

YES it works.

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.

The concept of instantaneous relative velocity should also work. The expression of the relative velocity given by you presupposes that the angle between the velocities of the two moving bodies is not changing...

Here that is not the case. The angle is not constant.. It is changing from moment to moment.

Yet I too feel that the expression of instantaneous relative velocity viz. Sqrt[U^2 - 2 U V cos a + V^2] should also give correct result.

Well I have not been able to really resolve the discrepancy pointed out by you. Maybe some Math-wizards like Acolyte would be able to plug the loop-hole correctly.

Originally posted by ranjan sinha
The concept of instantaneous relative velocity should also work. The expression of the relative velocity given by you presupposes that the angle between the velocities of the two moving bodies is not changing...

Here that is not the case. The angle is not constant.. It is changing from moment to momen ...[text shortened]... Maybe some Math-wizards like Acolyte would be able to plug the loop-hole correctly.

The cat doesn't know calculus, but it will cath up sure...