A-->B,B-->C,C-->D & D-->A. they all meet in the center. How far do they each walk? show you logic!!
2006-07-18 08:20:08 · 11 answers · asked by J S 1 in Science & Mathematics ➔ Mathematics
they ale always walking towards the next one. as a result they walk in a spiral shape
2006-07-18 08:39:01 · update #1
Each ant walks with same speed and towards its neighbour.
This means that the distances AB,BC,CD,DA are always the same. Also the angles between the ants are always the same : 90 degrees, because each ant walks towards its neighbour. Thus the ants are at any time on a corner of a square.
Because the velocity vectors of two neighbouing ants are orthogonal, the entire velocity of each ant is used to move towards the neighbouring ant. Since the initial distance is 1, each ant will walk 1 meter.
2006-07-18 09:01:46 · answer #1 · answered by gjmb1960 7 · 7⤊ 2⤋
This is a differential geometry problem (and calculus). I remember that you draw the paths of the 4 ants and then a square at some time t. I think that you have to mark the point (0,0) as the center of the square and write the ants points in terms of polar coordinates. (I don't have my notes with me at the moment, hope this helps.)
2006-07-18 08:28:01 · answer #2 · answered by raz 5 · 0⤊ 0⤋
They will walk in an Archimedes spiral to the centre, if they all walk at constant speed. The length of the spiral is independent of the speed they walk. The distance of one 'rotation' of the spiral is too tricky to type here without being able to point at things. I'd recommend Bronstein and Semendjajev's 'Handbook of Mathematics'. It's on page 106 of my edition...
2006-07-18 21:27:54 · answer #3 · answered by Sonia M 2 · 0⤊ 0⤋
They would all walk to the center in a curved line, corresponding to a circle with a diameter equal to that of the square.
Each ant would walk π/2 meters.
2006-07-18 08:28:04 · answer #4 · answered by MeteoMike 2 · 0⤊ 0⤋
Yeah you messed up your question. but if they ants walked toward the opposite corner they would each walk .7071 M
2006-07-18 08:51:43 · answer #5 · answered by matty b 2 · 0⤊ 0⤋
How do they get to the center if they are all walking to the next corners?
2006-07-18 08:24:58 · answer #6 · answered by gnomes31 5 · 0⤊ 0⤋
Are they walking straight to the center, or to another corner, then to the center? Your question is unclear.
2006-07-18 08:28:47 · answer #7 · answered by fredorgeorgeweasley 4 · 0⤊ 0⤋
the differential geometry dude is right but i'm buggered if i can work it out-think it ends up a spiral but don't know
2006-07-18 09:00:21 · answer #8 · answered by zebbedee 4 · 0⤊ 0⤋
how do they get to the center.they walkon the sides.so they wil never meet
2006-07-18 08:30:02 · answer #9 · answered by yiannis the greek 4 · 0⤊ 0⤋
four square.
2006-07-18 08:23:38 · answer #10 · answered by Anonymous · 0⤊ 0⤋