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 2006-12-20, 08:25 #1 mfgoode Bronze Medalist     Jan 2004 Mumbai,India 22×33×19 Posts Four heat seeking missiles Four heat seeking missiles are fired similtaneously from the four corners of a horizontal plane square formation of side 100 Km, high up in the air. They are all pointed to adjacent missiles in clockwise cyclic order so that they follow similar curved paths. Neglecting the effect of gravity, determine the distance travelled by each missile before they collide at the centre. hint: this problem is best done graphically and please display the curved path. Mally
 2006-12-20, 11:19 #2 axn     Jun 2003 2·2,423 Posts http://mathworld.wolfram.com/MiceProblem.html
2006-12-20, 17:09   #3
mfgoode
Bronze Medalist

Jan 2004
Mumbai,India

22·33·19 Posts
Mice

Quote:
 Originally Posted by axn1 http://mathworld.wolfram.com/MiceProblem.html

Thank you axn1. You are spot on. So for 4 what will be the distance ?
A question for the others.
Mally

 2006-12-20, 18:14 #4 Wacky     Jun 2003 The Texas Hill Country 44116 Posts Mally, You didn't specify that the missles all travel at identical speeds. However this is required for the curved paths to be "similar" in the strictest sense. The distance that each missle travels is 100 Km Last fiddled with by Wacky on 2006-12-20 at 21:36 Reason: Grammar
2006-12-21, 03:50   #5
drew

Jun 2005

2×191 Posts

Quote:
 Originally Posted by Wacky Mally, You didn't specify that the missles all travel at identical speeds. However this is required for the curved paths to be "similar" in the strictest sense. The distance that each missle travels is 100 Km
There's an interesting observation that can be made for the 'sqare' problem (not the general problem linked by axn1).

Each target's velocity is perpendicular to its pursuer's velocity, with no component from or towards the pursuer. Therefore, the distance is closed purely by the motion of the pursuer, which is directly toward the target. This explains why the path is exactly as long as the original side of the square.

Last fiddled with by drew on 2006-12-21 at 04:07

2006-12-21, 16:37   #6
mfgoode
Bronze Medalist

Jan 2004
Mumbai,India

22×33×19 Posts
same speeds

Quote:
 Originally Posted by Wacky Mally, You didn't specify that the missles all travel at identical speeds. However this is required for the curved paths to be "similar" in the strictest sense. The distance that each missle travels is 100 Km

You are quite right Wacky. My fault and omission of identical speeds

Mally

2006-12-21, 16:43   #7
mfgoode
Bronze Medalist

Jan 2004
Mumbai,India

40048 Posts
orthogonal

Quote:
 Originally Posted by drew There's an interesting observation that can be made for the 'sqare' problem (not the general problem linked by axn1). Each target's velocity is perpendicular to its pursuer's velocity, with no component from or towards the pursuer. Therefore, the distance is closed purely by the motion of the pursuer, which is directly toward the target. This explains why the path is exactly as long as the original side of the square.

Fine observation Drew. For the square, the velocity does not matter as it cancels out.
The general problem of axni1 was excellent.
Mally

 2006-12-21, 18:49 #8 Uncwilly 6809 > 6502     """"""""""""""""""" Aug 2003 101×103 Posts 22×72×47 Posts I say that they never intersept each other. In my world the square plane that you describe slices through Mt. Fuji. Once they get close enough to each other, the mountain obscures their view of each other. They wind up,, going around the mountain until they run out of fuel. Just finding a little hole.
2006-12-23, 08:31   #9
mfgoode
Bronze Medalist

Jan 2004
Mumbai,India

22·33·19 Posts
Little hole

Quote:
 Originally Posted by Uncwilly I say that they never intersept each other. In my world the square plane that you describe slices through Mt. Fuji. Once they get close enough to each other, the mountain obscures their view of each other. They wind up,, going around the mountain until they run out of fuel. Just finding a little hole.

In your world Maybe!

I have flown several times over Mt. Fuji every time we took off from Tokyo and it never obscured our view as we flew well above it, unlike Mt Blanc, where our Boeing 707 in 1966, crashed into it, and not a trace of it is left.

I was flying then and was happy not to have been on that ill fated flight.

Well as I understand you, yours is a terrestial oriented world, and I can well understand your viewpoint. Try shifting it higher than mountains and view the stars above. They are very much there too.!

Mally

2006-12-23, 08:34   #10
mfgoode
Bronze Medalist

Jan 2004
Mumbai,India

22·33·19 Posts
Interesting observation

Quote:
 Originally Posted by drew There's an interesting observation that can be made for the 'sqare' problem (not the general problem linked by axn1). Each target's velocity is perpendicular to its pursuer's velocity, with no component from or towards the pursuer. Therefore, the distance is closed purely by the motion of the pursuer, which is directly toward the target. This explains why the path is exactly as long as the original side of the square.

Your observation is correct.

Now Drew Im interested in solving it non graphically. Could you help ?

Mally

 2006-12-25, 10:15 #11 davieddy     "Lucan" Dec 2006 England 145128 Posts let x be the distance between two adjacent ants (missiles or whatever) dx/dt = 0 throughout. So x is the same as it started. David

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