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Optimisation question

  1. May 10, 2005 #1
    G'day guys, got this question out of Step-by-step calculs by J.G. graham for those of you who have the book.

    I've had quite a bit of a play around with it but it doesn't seem to be going anywhere i end up with a few equations which have 3 variables, and i can't reduce it to two.

    Okay here's the question.

    In rugby, how far back from the tryline should the kicker take the ball to ave the best chance of converting the try?

    Take the ball back until the angular width of the goalposts as seen by the kicker is a maximum. Let L be the width of the goalposts, let the try(touchdown thing) be scored a distance h (measured along the tryline EF) from the left hand goalpost (A) and let x be the distance the ball is take back perpendicular to the tryline, as shown in the diagram.

    the field is 69 x 100 m and the width of the goalposts (L) is 5.6 m. Find the optimal position of the kicker inorder for him to have the largest angle to kick the ball through the posts.
     

    Attached Files:

  2. jcsd
  3. May 10, 2005 #2

    HallsofIvy

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    Yes, that's exactly what you want to do!

    According to your picture, tan(angle BCD)= (h+l)/x so angle BCD= arctan((h+l)/x)
    tan (angle ACD)= h/x so angle ACD= arctan(h/x). Therefore, angle BCA= angle BCD- angle ACD= arctan((h+l)/x)- h/x. h and l are constants, differentiate that with respect to x and set equal to 0.
     
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