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Thread: multi-variable ballistic optimization

  1. #1
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    Question multi-variable ballistic optimization

    A material point slides up a ramp of length l making an angle α = 30° with the horizontal. Its initial speed (at the bottom of the ramp) is 10m/s. This point is subject to gravity with g = 9.81m/sē. At the top of the ramp the material point starts a free fall and falls on the ground with a reach multi-variable ballistic optimization-image-4.jpg

    The goal is to get the ramp length that maximizes that reach. What is this length?

    I don't know how to begin
    Any suggestions ?
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  2. #2
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    Re: multi-variable ballistic optimization

    You posted this under "Advanced Algebra" but there is no "Advanced Algebra" here. (Nor is it "mult-variable. The only variable is l. The rest are constants.) I would treat it as a Calculus problem- take the derivative of the function with respect to l, set that equal to 0, and solve for l.
    Last edited by HallsofIvy; Oct 21st 2018 at 12:33 PM.
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  3. #3
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    Re: multi-variable ballistic optimization

    Quote Originally Posted by HallsofIvy View Post
    Then do what I presume you learned in Calculus- take the derivative with respect to l, set it equal to 0, and solve for l.
    only problem with that is that this is the advanced algebra forum....
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  4. #4
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    Re: multi-variable ballistic optimization

    Yes, but there was no "Advanced Algebra" in the problem! I have edited my response.
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  5. #5
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    Re: multi-variable ballistic optimization

    Quote Originally Posted by HallsofIvy View Post
    Yes, but there was no "Advanced Algebra" in the problem! I have edited my response.
    Ha! That is one way to handle it.

    Using calculus it can be shown that the optimal length of the ramp is twice the x coordinate of the vertex of the quadratic in the radical.

    That is $\ell = \dfrac{2v_0^2}{3g}$
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