1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Where did I go wrong?

  1. Feb 15, 2006 #1
    An extreme skier, starting from rest, coasts down a mountain that makes an angle 25.0° with the horizontal. The coefficient of kinetic friction between her skis and the snow is 0.200. She coasts for a distance of 13.4 m before coming to the edge of a cliff. Without slowing down, she skis off the cliff and lands downhill at a point whose vertical distance is 3.20 m below the edge. How fast is she going just before she lands?

    W= Fn*13.4

    Fn*13.4= .5mv^2

    (mg sin25 - (.200)(mg cos25))(13.4)= .5mv^2

    (g sin25 - (.200)(g cos25))(13.4)= .5v^2

    ((9.8) sin25 - (.200)((9.8) cos25))(13.4)= .5v^2

    31.6949624131 = .5v^2

    2(31.6949624131) = v^2

    sqrt (63.3899248261) = v

    7.96177899882 = v
    Vy= 7.96177899882 (sin25)

    Vy= 3.36479320085

    Vy = sqrt (3.36479320085^2 + 2(-9.8)(-3.2))

    Vy = 8.604756 m/s
  2. jcsd
  3. Feb 15, 2006 #2

    Doc Al

    User Avatar

    Staff: Mentor

    I didn't check your calculations, but it looks like you calculated the y-component of the final velocity. What happened to the x-component?

    Tip: No need to find components of the velocity; you can use energy conservation to find the final speed.
  4. Feb 15, 2006 #3
    do I need the x? Because once it goes into free fall it is only accelerating in the y direction.

    "you can use energy conservation to find the final speed"
    I am confused by what you mean.
  5. Feb 15, 2006 #4

    Doc Al

    User Avatar

    Staff: Mentor

    You are correct that only the y-component will accelerate, but the x-component of the velocity is needed to find the total velocity at the bottom. (It's just [itex]v^2 = v_x^2 + v_y^2[/itex].)

    At the point that the skier leaves the cliff, she has a speed (which you figured out) and thus a kinetic energy. She also has gravitational PE compared to her landing point. Energy is conserved as she falls. (Gravitational PE is converted to KE as she falls.)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook