Wednesday, November 18, 2009

Fox 187

7 comments:

  1. I am in full agreement with Newzad. Here's my solution -- Given: y=x^2/4-2x+8, dy/dx = x/2 - 2 which for maximum range must equal tan(α) = tan(45) = 1. This gives us: x/2 -2 = 1 or x = 6 or B is (6,5). Now with B as origin we've: y = xtan(α)-(g/2)(x/ucos(α))^2 where α = 45 deg. and u^2= 2*g*(8 - 5)= 6*g or y= x - x^2/6. In the original frame of reference, our equation:
    y - 5 =(x -6)-(x -6)^2/6
    If we set y=0 in this equation of parabolic motion, we get x= (9 - V39) or (9 + V39) where V = square root. The first root is clearly inadmissible hence x = 9 + V39 ~ 15.245
    Ajit

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  3. The options will be updated. Thanks for your input. I made a simple error: Instead of R = x + Vx(t1+t2), I wrote R = x + Vx(t2), that's why 12 or 13 is very short.

    BUT the solution is NOT 15.245.
    Believe me the solution is NOT 15.245.
    Still not confirmed yet but I have a solution bigger than 15.245. It's amazing!
    Good luck !

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  4. Hi,
    Along the lines suggested by you, I set up the following equation:-y=z(R-x)-u(R-x)^2/(4(8-y)) where y=x^2/4-2x +8, tan(α)=z=x/2-2 & (sec(α))^2=u=1+z^2 and R is the range. By varying x, I found that at x=16/3, y=40/9 the range is exactly 16 and I think that's the maximum. In our equation if we put x=6 we get R=15.2445 as b4 which is clearly not the highest possible.
    Thanks for the nice problem!
    Ajit

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  5. YES, 16 is the answer for the maximum range.
    Thank you Ajit.

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  6. Yes Yuv-k, 16 is the answer. But it doesn't depend on g. As long as there is a positive gravity, the answer is the same. In other words, Max range is 16 on Earth, Jupiter as well as on Pluto.

    As a side note: those who degraded Pluto from planet to dwarf will pay dearly for their arrogance :(

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