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College Calculus

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A light is on the ground 20m from a barn. A 2m tall llama walks from the light directly toward the side of the barn at 1m/s. How fast is the height of the llama's shadow on the barn changing when he's 14m from the barn? (draw and label a nice diagram first!)

  • College Calculus -

    If x is the diatsnace from the light to the llama, and h is the height of the shadow on the wall, then using similar triangles,

    h/20 = 2/x
    hx = 40

    At 14m from the barn, x=6 and h = 40/6 = 20/3

    hx' + xh' = 0
    (20/3)(1) + 6h' = 0
    h' = -10/9

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