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28 August, 18:29

Starting from rest, a 30.8 kg child rides a 9.75 kg sled down a frictionless ski slope. At the bottom of the hill, her speed is 6.0 m/s. If the slope makes an angle of 15.1 ° with respect to the horizontal, how far along the hill did she slide on her sled?

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  1. 28 August, 22:26
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    s = 7.044 m

    Explanation:

    Given:

    - The mass of child Mc = 30.8 kg

    - The mass of sledge Ms = 9.75 kg

    - The slope θ = 15.1°

    - The speed of of sledge at bottom vf = 6.0 m/s

    - The initial velocity at top vi = 0

    Find:

    - We will apply the conservation of energy principle on the system consisting of child and sledge. The change in potential energy ΔP. E of the system from top to bottom gives rise to change in kinetic energy ΔK. E.

    ΔP. E = ΔK. E

    (Mc + Ms) * g*h = 0.5 * (Mc + Ms) * (vf^2 - vi^2)

    Where, h: the change in vertical height

    h = 0.5 * (vf^2 - vi^2) / g

    h = 0.5*vf^2 / g

    h = 0.5*6.0^2 / 9.81

    h = 1.835 m

    - The distance traveled along the slope (s) can be calculated by trigonometric ratio:

    sin (θ) = h / s

    s = h / sin (θ)

    s = 1.835 / sin (15.1)

    s = 7.044 m
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