any help to solve this problem will be truly appreciated

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Asssume that predator A , travelling at a speed of "d"mph, is pursuing prey B, which is travelling at a speed of "e"mph.In addition assume that A begins (at time t=0)at the origin and pursue B which begins at the point(b,o),b>0 and travel up the line x=b. After t hour A is located at point (x,y).In addition it is assumed that A is always heading directly at B.Our goal is to find Y as a function of X. This problem is related to curve of pursuit

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http://mathworld.wolfram.com/PursuitCurve.html

Gautam B.

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Interesting!

almirah

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Su..uit This problem looks really ugly to me. Btw which college u go in? STANFORD

zalimSingh

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lemme put my geek hat on. oh yeah... my intuition tells me that that A will NEVER reach B if it is always heading directly at B. It will only reach B asymptotically. lemme figure out the math and see if it jives with my intuition....this should not be too hard.

zalimSingh

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well it turns out that a parametrized solution is the way out, as shown by the folks working at wolfram. i still believe that A never catches B with this strategy. the strategy for A is is to aim slightly ahead at B's future location. this again works only if d > e.

zalimSingh

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yup...if you look at equation (24). in the limit t ---> infinity, the term inside the square brackets --> 1, so x approaches x_0, which is the line that B will always be on. In order to catch B, a necessary condition for A is to have an x coordinate that equals B's x coordinate. This occurs only in the limit, so A never catches B. bisho, i did not answer your question directly, but your question made me think about something else. so kudos for that.

bisho

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thyanx for ur answer zalim sing but thta 's not exactlywhat i am looking, it can catch ,it's actually difeerential equation and slope of tangent equals to dy/dx i believe

zalimSingh

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it can catch??? r u sure? i just laid out a sketch of a proof that it does not. i can prolly explain it in words better.... say you aim a bullet at a bird. as soon as the bird hears the gun shot, it flies away...the bullet takes some time to travel to the bird, so during this time, the bird will have travelled away from its initial location, and so does not get killed. (this is an extreme example, because in reality, the bird's response time is less than the time for the bullet to get to it, which is why it gets killed). the exact same thinking can be applied to your example to show why A will never catch B... but anyway, dont know if you had a chance to check out the readily-available solution to your problem set at: - http://mathworld.wolfram.com/PursuitCurve.html anyway, good luck.

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