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Math Help - Another mechanics question.

  1. #1
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    Another mechanics question.

    In the figre the curve AB is a snow slope mounted on a frame used for ski jumping practice. Skiers start from rest at A, 30 metres above the horizontal ground and launch themseves into the air from B, 10 meters above the ground at 10 degrees. C is vertically below B and D is the point the skier will land if no air resistance/friction
    Im guessing you use potential energy and kinetic energy to find V.
    I then find V as 14m/s...
    The answer is 35.5cm which im struggling to get.
    The red part on the diagram is the projection.
    Any help is appreciated.
    Thanks
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  2. #2
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    Quote Originally Posted by AshleyT View Post
    Im guessing you use potential energy and kinetic energy to find V.
    I then find V as 14m/s...
    The answer is 35.5cm which im struggling to get.
    The red part on the diagram is the projection.
    Any help is appreciated.
    Thanks
    First we need to convert all units into meters .

    then we have that mg \Delta h =\frac{1}{2}mv^2 \iff v=\sqrt{2g \Delta h}=\sqrt{2g(.2)} \approx 1.97989

    This is the velocity at take off. Now the skier is a projectile

    Now in the horizontal direction the only force is mass times gravity. Using the kinemetic equations to find when the skier hits the ground we get

    0=.1+1.97989\sin(10^\circ)t-\frac{1}{2}(9.8)t^2

    Solving for t t \approx .18218

    Now in the x direction there are no forces so we get

    x=1.97989\cos(10^\circ)(.18218) \approx 0.35522

    dont forget that the above answer is in meters and (unlike me) don't surpress your units. So we get 35.5 cm
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    Ah, thankyou very much. I was doing the right thing but wrong values =/...
    Last edited by AshleyT; June 13th 2009 at 02:56 AM.
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