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Old 2006-12-20, 08:25   #1
mfgoode
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Question 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
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Old 2006-12-20, 11:19   #2
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http://mathworld.wolfram.com/MiceProblem.html
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Old 2006-12-20, 17:09   #3
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Thumbs up Mice

Quote:
Originally Posted by axn1 View Post
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
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Old 2006-12-20, 18:14   #4
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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
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Old 2006-12-21, 03:50   #5
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Quote:
Originally Posted by Wacky View Post
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
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Old 2006-12-21, 16:37   #6
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Thumbs up same speeds

Quote:
Originally Posted by Wacky View Post
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
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Old 2006-12-21, 16:43   #7
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Thumbs up orthogonal

Quote:
Originally Posted by drew View Post
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
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Old 2006-12-21, 18:49   #8
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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.
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Old 2006-12-23, 08:31   #9
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Cool Little hole

Quote:
Originally Posted by Uncwilly View Post
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
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Old 2006-12-23, 08:34   #10
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Default Interesting observation

Quote:
Originally Posted by drew View Post
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
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Old 2006-12-25, 10:15   #11
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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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