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Originally posted by PBE6Allan Curry's solution and Tristan Simbulan's solutions are rather lengthy. Second order derivatives are involved indeed.
Alan Curry --> http://mathproblems.info/group2.html (see problem #30)
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...
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Originally posted by ranjan sinhaWhy don't you talk about your own method?
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...
Originally posted by ranjan sinhaif its only three lines could someone reproduce them here so us non-physicist types could see too. thanks
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...
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Originally posted by aginisHere they are;...Let T be the time required.
if its only three lines could someone reproduce them here so us non-physicist types could see too. thanks
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 ranjan sinhaYES it works.
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.
Originally posted by howzzatThe 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...
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.
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 sinhaThe cat doesn't know calculus, but it will cath up sure...
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.