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28 March, 21:24

What is tarzan's speed vf just before he reaches jane? express your answer in meters per second to two significant figures?

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  1. 28 March, 21:34
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    Before swinging, T has only potential energy, (no speed)

    Ui = mgh

    Where h is the vertical displacement of T

    From the laws of geometry,

    cos45 = (L-h) / L

    cos45 = 1-h/L

    h/L = 1-cos45

    h = L (1-cos45)

    Therefore

    Ui = mgL (1-cos45)

    Proceeding the same way,

    Twill raise to aheight of h' due to swing

    h' = L (1-cos30)

    The PE of T after swing is

    Uf = mgh'

    Uf = mgL (1-cos30)

    Along with the PE, T has some kinetic energy results due to the moment.

    Tf = 0.5*mv^2

    According to the law of conservation of energy,

    Ui = Uf+Tf

    mgL (1-cos45) = mgL (1-cos30) + 0.5*mv^2

    gL (co30-cos45) = 0.5*v^2

    9.8*20 * (co30-cos45) = 0.5*V^2

    v = 7.89 m/s

    The speed f T after swing is 7.89 m/s
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