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Math Help - At what thime will the bullet be 192 feet in the air?

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    At what thime will the bullet be 192 feet in the air?

    A bullet is fired into the air with an initial upward velocity of 80 feet per second from the top of a building 96 feet high. The equation that gives the height h of the bullet at any time t is h=96+80t-16t^2. At what thime will the bullet be 192 feet in the air?
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    Quote Originally Posted by Alienis Back View Post
    A bullet is fired into the air with an initial upward velocity of 80 feet per second from the top of a building 96 feet high. The equation that gives the height h of the bullet at any time t is h=96+80t-16t^2. At what thime will the bullet be 192 feet in the air?
    It starts at 96ft. It is moving at 80 ftps.

    h = 96 + 80t -16t^2

    So we need another 96ft to reach. So we need 192 = 96 + 80t - 16t^2

    In other words, 96 = 80t - 16t^2

    in other words, 96 + 16t^2 = 80t

    in other words, 16t^2 = 80t - 96

    so.... basically, t^2 = 5t - 6

    so essentially, 3^2 = 9 = 5 x 3 - 6

    so basically t = 3

    so fundamentally .... 196 = 96 + 240 - 144

    so ummm...the time is 3 seconds................lol i think
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    Quote Originally Posted by Alienis Back View Post
    A bullet is fired into the air with an initial upward velocity of 80 feet per second from the top of a building 96 feet high. The equation that gives the height h of the bullet at any time t is h=96+80t-16t^2. At what time will the bullet be 192 feet in the air?
    That will happen twice. Once on the way up, and once on the way down.

    -16t^2+80t-96=192

    Simplifying,

    -t^2+5t-6=0

    t^2-5t+6=0

    Solve the quadratic for for the two times (t).
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  4. #4
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    Lol, silly me not seeing that it was a quadratic equation.

    Complete answer for OP:

    (t - 3)(t - 2) = 0

    therefore t = 3 or t = 2.... but as it is going up and then down, 3 and 2 are your answers!
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    Thank you guys
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