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Skier on a Slope - Find Total Distance

  1. Feb 27, 2010 #1
    1. The problem statement, all variables and given/known data

    Starting from rest, a 75 kg skier slides down a 17.0 º slope. If the coefficient of kinetic friction between the skis and snow is
    0.120 and it takes 28.2 s to get to the bottom, how long is the ski trail?

    2. Relevant equations

    [tex]F = ma[/tex]
    [tex]s_f = s_i +v_i + 1/2at^2[/tex]

    3. The attempt at a solution

    I drew a diagram and came up with this:

    The acceleration of the skier down the slope is mgsin(17) the friction going the opposite direction is mgsin(17)0.120.

    F_net is mgsin(17)-mgsin(17)0.120

    Taking F=ma and solving for a I came up with F/m=a

    So....[mgsin(17)-mgsin(17)0.120]/m

    This gave me 2.52 m/s^2

    Plugging that into one of my kinematic equations....

    [tex]s_f = s_i +v_i + 1/2at^2[/tex]

    s=(.5)(2.52)(28.2^2)

    I ended up with the final distance as 1002m.

    The book answer is 692m.

    What am I missing?
     
  2. jcsd
  3. Feb 27, 2010 #2
    Remember that the normal (for dealing with the friction) is going to involve cosine, not sine.
     
  4. Feb 27, 2010 #3
    Duh.

    Yep, that was it.

    Thank you.
     
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