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March 29, 2017

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A ball is thrown from an initial height of 2 meters with an initial upward velocity of 25m/s. The ball's height h (in meters) after t seconds is given by the following.

Find all values of t for which the ball's height is 12 meters.
Round your answer(s) to the nearest hundredth.

  • Algebra - ,

    h(t) = 2+25t-4.9t^2
    h=12 when

    2+25t-4.9t^2 = 12
    t= 0.44 and 4.66 seconds

  • Algebra - ,

    To find when the ball's height is
    7
    meters, we substitute
    7
    for
    h
    and solve for
    t
    .
    =7+2−25t5t2
    In order to solve for
    t
    , we first rewrite the equation in the form
    =+at2+btc0
    .
    =+−5t225t50
    Next, we use the quadratic formula to solve for
    t
    .
    =t−b±−b24ac2a
    Our equation has
    =a5
    ,
    =b−25
    , and
    =c5
    .
    Another way
    We use these values in the formula.
    t
    =−−25±−−252·4·55·25
    =25±52510
    We get that
    t
    can be either of two values to solve the equation.
    =t=−25525100.2087…
    or
    =t=+25525104.7912…
    Rounding these values to the nearest hundredth, we get
    =t0.21
    or
    =t4.79
    .
    So, the ball's height is
    7
    meters at approximately
    0.21
    seconds (on its way up) or
    4.79
    seconds (on its way down).

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