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Old 05-12-2005, 12:47 AM
laurencekarl
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Heh. Good job. Did you try to submit your score? Mine wouldn't go through. I imagine that it was trying to load several million scores and choked.

Of course but as economists like to say, "all else being equal." There could (probably is) be an optimal set of explosions (input of kinetic energy) that would overcome the optimal launch angle. The reason for 45 degrees is that in 2D velocity, position, etc. are vectors. So distance in the x direction is the result of an interplay between kinetic energy and the acceleration of gravity (that is expended in both the x and y directions) so by maximizing x it turns out that you have to balance the fact that the cat is heading towards the earth (gravity) with the fact that past a certain angle you will go farther up (y direction) at the expense of going less far in the x direction (distribution of kinetic energy between the two directions). I assume that there are more clever ways of showing it but by setting the differential of the position (or velocity) function in terms of the x component equal to 0 and then solving for x you will find the maximum x distance that can be achieved. Off the top of my head and I would be embarrased if that where wrong but I think that's the technique would work or at least going in that general direction would. I think that when one considers the effects of wind that it is about 23 degrees.
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