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31 January, 15:13

Tarzan runs at 6 m/s and grabs a vertical vine (negligible mass) 4.1 m long which is tied to a tree at the top. Tarzan swings up.

Determine the maximum height Tarzan will swing up and the angle the vine makes respect to vertical.

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  1. 31 January, 18:36
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    v = velocity of Tarzan at the bottom as he grabs the vertical vine = 6 m/s

    L = length of vine tied to tree at the top = 4.1 m

    h = maximum height gained by Tarzan = ?

    m = mass of Tarzan

    using conservation of energy

    maximum potential energy at the top = kinetic energy at the bottom

    mgh = (0.5) m v²

    gh = (0.5) v²

    (9.8) h = (0.5) (6) ²

    h = 1.84 m

    BC = h = height = 1.84 m

    AC = length of vine = 4.1 m

    AB = AC - BC = 4.1 - 1.84 = 2.26 m

    In triangle ABD

    Cosθ = AB/AD

    Cosθ = 2.26/4.1

    Cosθ = 0.55

    θ = Cos⁻¹ (0.55)

    θ = 56.6 deg
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