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How to find the optimum angle for takeoff for ski jump using

  1. Mar 8, 2017 #1
    1. The problem statement, all variables and given/known data
    I need to find how to find the optimum angle for take off on the ski flying hill using projectile motion. and why?

    2. Relevant equations
    formula-for-trajectory-of-projectile-motion.png

    3. The attempt at a solution

    I'm just confused, because would I just use all the formulas above to solve the problem? or do I have to create another formula?
    The optimum angle would result in the maximum horizontal range, right?
    We know the time of flight = 2Vyi/g so the range = Vxi*2Vyi/g = 2Vi²/g *sinΘ*cosΘ =
    R(Θ) = 2Vi²/g *sinΘ*cosΘ = Vi²/g *sin2Θ
     
    Last edited: Mar 8, 2017
  2. jcsd
  3. Mar 8, 2017 #2

    haruspex

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    The first and last equations you quote assume landing at the same height as take-off. Is that case in your question?
    (Always best to quote the whole question word for word in your post, in case you have misinterpreted something.)
     
  4. Mar 8, 2017 #3
    so how would I write it if the landing it different from the takeoff?
     
  5. Mar 8, 2017 #4

    haruspex

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    Go back to the more fundamental ("SUVAT") equations from which those are derived.
     
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