Anonymous
Anonymous asked in Science & MathematicsMathematics · 8 years ago

A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a spe?

A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 4 ft/s along a straight path. How fast is the tip of his shadow moving when he is 30 ft from the pole?

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  • 8 years ago
    Favorite Answer

    Let S denote the length of the shadow.

    When he's F feet from the pole, you have

    6/15 = x/(F+x), where x = S - F

    2(F+x) = 15x

    2F = 13x, so

    S = F + (2F/13) = 28F/13

    dF/dt = 4 ft/s

    dS/dF = 28/13

    dS/dt = (dS/dF) (dF/dt) = (112/13) ft/s

    = about 8.6 ft/s

  • cidyah
    Lv 7
    8 years ago

    See the figure:

    http://s1169.photobucket.com/user/chibuckt/media/I...

    X = Xp+Xs

    dXp/dt = 4 ft/s (given)

    dX/dt = ?

    Using similar triangles, 6/Xs = 15/X

    6/Xs = 15/(Xp+Xs)

    6(Xp+Xs) = 15Xs

    15Xs = 6Xp+6Xs

    9Xs = 6Xp

    Xs = (6/9) Xp

    Xs + Xp = (6/9) Xp + Xp

    X = (15/9) Xp

    dX/dt = (15/9) dXp/dt

    dX/dt = (15/9)(4) = 6.667 ft/s

    The tip of his shadow is moving 6.667 ft/s regardless of how far away he is from the base of the pole.

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