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Math Help - Height of a ball Word Problem!

  1. #1
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    Height of a ball Word Problem!

    Hello everyone,

    I'm stuck on this problem and would love an explanation:

    If a ball is thrown into the air at 64 feet per second from the top of a 100 foot tall building, its height can be modeled by the function
    S=100+64t-16t(squared), where S is in feet and t is in seconds.


    Find the max height the ball will reach??


    Thanks
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  2. #2
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    Quote Originally Posted by Annb View Post

    If a ball is thrown into the air at 64 feet per second from the top of a 100 foot tall building, its height can be modeled by the function
    S=100+64t-16t(squared), where S is in feet and t is in seconds.

    Find the max height the ball will reach??
    the graph formed by s(t) = 100+64t-16t^2 is an inverted parabola ... the ball reaches its maximum height at the vertex of that parabola.

    does the expression \frac{-b}{2a} ring a bell ?
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  3. #3
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Annb View Post
    Hello everyone,

    I'm stuck on this problem and would love an explanation:

    If a ball is thrown into the air at 64 feet per second from the top of a 100 foot tall building, its height can be modeled by the function
    S=100+64t-16t(squared), where S is in feet and t is in seconds.


    Find the max height the ball will reach??


    Thanks
    Well, this - s(t)=100+64t-16t^2 - is simply a parabola that opens downward. Do you know how to find the vertex?
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  4. #4
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    no : (
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  5. #5
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Annb View Post
    no : (
    You may need a refresher. Check out these links:

    Vertex of a Parabola

    The Vertex of a Parabola
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  6. #6
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    is it y=ax squared + bx + c?
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  7. #7
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Annb View Post
    is it y=ax squared + bx + c?
    Yes, that is the standard equation of a parabola.

    So, in your case...what are the values a,b, and c?
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  8. #8
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    a=100
    b=64
    c=16
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  9. #9
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Annb View Post
    a=100
    b=64
    c=16
    No. a is always the number beside the squared variable. b is always the number beside the first degree variable, and c is always the constant term.

    So

    a=-16
    b=64
    c=100.

    Do you understand?

    Now, use the formula for finding the vertex. Do you know it?
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  10. #10
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    is it -b/2a?
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  11. #11
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Annb View Post
    is it -b/2a?
    Very good. But, that's not the whole story. This will give you the time at which the object will reach its maximum height. So...what do you have to do once you have this time?
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  12. #12
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    Ok, so I when I did the equation I got the answer -2. I just apply it to the equation and substitute t for -2 and i got 164!! The answer..


    Thank you
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  13. #13
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Annb View Post
    Ok, so I when I did the equation I got the answer -2. I just apply it to the equation and substitute t for -2 and i got 164!! The answer..


    Thank you
    Well... almost right. Let me ask you a question: Can time ever be negative? The answer is no (at least in this context).

    \frac{-b}{2a}=\frac{-(64)}{2(-16)}=\color{red}{+}2.

    Now, plugging back in we have

    s(2)=100+64(2)-16(2)^2

    =100+128-64

    =164.

    Sorry for being picky, but precision is key in mathematics.

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