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A model rocket is launched with an initial velocity of 212ft/sec. It's height h, in feet, after t seconds is given by the formula h=212t-16t^2. After how many seconds will the rocket first reach a height of 592ft?

  • Math -

    To get the time, we just substitute h = 592 to the equation:
    h = 212t - 16t^2
    592 = 212t - 16t^2
    16t^2 - 212t + 592 = 0
    4t^2 - 53t + 148 = 0
    Factoring,
    (t - 4)(4t - 37) = 0
    t = 4 s
    t = 37/4 s
    Since it requires the time in which the rocket FIRST reaches a height of 592, we choose the smaller, which is t = 37/4 s.

    Hope this helps :3

  • Math-correction -

    *lol I'm sorry the smaller time is t = 4s. OMG XD

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