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Math Help - quadratic problem

  1. #1
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    fratta terme forli Italy
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    quadratic problem

    I have this problem with equation h=15+20t-2t^2 object throwen from tower

    I must making graph to show time of flight
    Then show greatest height reached.
    How high is building
    And how long did it take for object to hit.

    1 I thinking for graph formula must be xv=-b/2a
    which is -20/-2x2=-20/-4=5 this is for my x.
    can you please showing me how for getting my y .

    when i am knowing this i think i can do rest of problems,

    Thanksing you
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  2. #2
    MHF Contributor
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    Umm, you are using formulas to find the vertex of the parabola of the flight of the object.

    y = ax^2 +bx +c -------(i), parabola
    x of vertex = -b/(2a)
    y of vertex = c -(b^2)/(4a)

    So,
    h = 15 +20t -2t^2 ------parabola
    Rearrange that to be in the form of (i) above,
    h = -2t^2 +20t +15 ----------(ii)

    t of vertex = "-b/(2a)" = -20/(2(-2)) = 5 ------which you got.
    h of vertex = "c -(b^2)/(4a) = 15 -[(20^2)/(4(-2))] = 15 +50 = 65
    Therefore, greatest height reached is 65 units.

    How high is the building?
    When time t is zero, or when ball is not thrown yet,
    h = 15 +20t -2t^2
    h = 15 +20(0) -2(0)^2
    h = 15 units ---------------height of building.

    And how long did it take for object to hit.
    To hit the ground?
    That will be if h = -15 units. (The negative sign is to show only that the distance is measured opposite the positive measurements.)
    Because the gr4ound is 15 units below the top of the building---where t begins.
    So,
    -15 = 15 +20t -2t^2
    Put them all to the lefthand side,
    2t^2 -20t -15 -15 = 0
    2t^2 -20t -30 = 0
    t^2 -10t -15 = 0

    Umm, can you take over now?
    Use the Quadratic formula to find t when the object hit the ground. It is t = 11.3245 units time.

    If you like, check that against h = 15 +20t -2t^2. See if you you can get h = -15.
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  3. #3
    Super Member

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    Lexington, MA (USA)
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    Hello, gregorio!

    Equation: . h\:=\:15+20t-2t^2, object thrown from tower

    I must make a graph to show time of flight.
    (a) Then show greatest height reached.
    (b) How high is building?
    (c) How long did it take for object to hit?

    We have a parabola: . h \:=\:-2t^2 + 20t + 15
    . . So: . a = -2,\;b = 20,\;c = 15

    Then the vertex is at: . t \:=\:\frac{-b}{2a} \:=\:\frac{-20}{2(-2)} \:=\:5
    . .
    It reaches maximum height in 5 seconds.

    Hence: . h \:=\:-2(5^2) + 20(5) + 15 \:=\:65
    . .
    The maximum height is 65 feet.


    (b) How high is the building?
    Hint: Where was the object at the very beginning (t = 0)?


    (c) When does it strike the ground?
    Hint: When does the object have zero height (h = 0)?
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