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Math Help - Another Quadratics Word Problem (grade 11)

  1. #1
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    Another Quadratics Word Problem (grade 11)

    Here's that other question. (I'm not trying to get anyone to do the work for me, it's just that the 3 questions are due tomorrow and I'm like this ...)

    ================================================== ==


    A warning flare is fired vertically from the top of a tower. It's height h in metres after t is given by the equation h = 10 + 40t - 5t

    A) how high is the tower

    *For this I substituted t for 0(zero) and got an answer of 10m.





    B) what height is reached by the flare.

    *For this I "completed the square" and got "h=-5(t-4) + 78"...don't know if that's right of what to do after*





    C) how long is it in the air (until it hits the ground)

    I have no idea here
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  2. #2
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    Re: Another Quadratics Word Problem (grade 11)

    Quote Originally Posted by tdotodot View Post
    Here's that other question. (I'm not trying to get anyone to do the work for me, it's just that the 3 questions are due tomorrow and I'm like this ...)

    ================================================== ==


    A warning flare is fired vertically from the top of a tower. It's height h in metres after t is given by the equation h = 10 + 40t - 5t

    A) how high is the tower

    *For this I substituted t for 0(zero) and got an answer of 10m.
    Assuming that the flare was fired at t= 0, yes. That's a reasonable assumption but the problem should have said something like "in metres t seconds after firing".





    B) what height is reached by the flare.

    *For this I "completed the square" and got "h=-5(t-4) + 78"...don't know if that's right of what to do after*
    It's easy enough to check: (t- 4)^2= t^2- 8t+ 16 so -5(t-4)^2= -5t^2+ 40t- 80 and -5(t-4)^+ 78= -5t^2- 40t- 2. No, that's not the same thing as 10+ 40t- 5t^2.
    10+ 40t- 5t^2= 10- 5(t^2- 8t)= 10- 5(t^2- 8t+ 16- 16)= 10- 5(t- 4)^2+ 80= 90- 5(t- 4)^2

    Now you know, I hope, that a square is never negative so -5(t-4)^2 is never positive and the height is always less than to equal to its value when t= 4.



    C) how long is it in the air (until it hits the ground)

    I have no idea here
    In your answer to a, you said that the tower was 10 metres above the ground since h(0)= 10.
    That means you are taking h= 0 at the ground. Solve the equation 10+ 40t- t^2= 0
    Last edited by HallsofIvy; October 12th 2011 at 02:08 PM.
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