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Math Help - Solve the equation. Round to the nearest tenth, if necessary.

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    Solve the equation. Round to the nearest tenth, if necessary.

    If an object is projected upward with an initial velocity of 64 feet per second from a height of 336 feet, then its height t seconds after it is projected is defined by the expression h(t) = -16t2 + 64t + 336. How long after it is projected will it hit the ground?


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    Quote Originally Posted by cechmanek32 View Post
    If an object is projected upward with an initial velocity of 64 feet per second from a height of 336 feet, then its height t seconds after it is projected is defined by the expression h(t) = -16t2 + 64t + 336. How long after it is projected will it hit the ground?


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    Since h(t) is the height of the object we want h(t)=0 that is

    -16t^2+64t+336=0 \iff -16(t^2-4t-21)=0 \iff -16(t-7)(t+3)=0

    So t=7 or t=-3 since we are concerned with only future events we don't use t=-3. So the object hits the ground after 7 seconds.

    Good luck.
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    Hello,

    Quote Originally Posted by cechmanek32 View Post
    If an object is projected upward with an initial velocity of 64 feet per second from a height of 336 feet, then its height t seconds after it is projected is defined by the expression h(t) = -16t2 + 64t + 336. How long after it is projected will it hit the ground?


    THANK YOU!!!
    Find t such that h(t)=0.

    h(t)=-16t^2+64t+336=16(-t^2+4t+21)=-16(t-7)(t+3)


    t=7 or t=-3.

    Because it's a nonsense to have a negative duration, the solution is 7seconds...



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