calculus

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The three pigls are building their houses while the brik=ck house building pig and the stick house building pig are working at a steady rate, the straw house building pig(knowing the wolf will arrive first at his house) is frantically increasing his rate of building by 2feet/minute. the straw house building pig has to make his house 16 ft tall(right now, it's 0 feet tall) and the wolf is scheduled to arrive in 5 minutes. Will the pig have his house built for the wolf to blow down by the time he arrives?

  • calculus -

    are you sure this is a question?

  • calculus -

    this is just a standard acceleration problem.

    s = 1/2 at^2
    16 = 1/2 * 2 * t^2
    16=t^2
    t=4

    so, in 4 min the house will be 16' tall, and he will be (briefly) safe.

  • calculus -

    now, if you want to use your calculus, let f(t) be the height of the house after t minutes.

    f ''(t) = 2

    f '(t) = 2t + c
    f '(0) = 0 means c=0 and
    f '(t) = 2t

    f(t) = t^2+c
    f(0) = 0 means c=0, so
    f(t) = t^2

    16 = t^2
    t=4

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