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March 26, 2017

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the function is h(t)= -4.9t^2+2t+45 (t represents time in seconds and h represents height in metres.)
a) how tall is the building?
b) how long does it take the balloon to fall on the sidewalk?
c)determine the max height of balloon

  • Math - ,

    What building?
    And where does the balloon come in ?

  • Math - ,

    The question states that the water balloon is thrown from the roof of a building. the path that the balloon follows the following function, which was listed above

  • Math - ,

    Ok,
    a) so when the balloon was thrown from the building
    t = 0
    so h = 0 + 0 + 45
    The building is 45 metres high

    b) when it hits the ground, h = 0
    0 = -4.9t^2 + 2t + 45
    4.9t^2 - 2t - 45 = 0
    by the formula:
    t = (2 ± √(4 - 4(4.9)(-45))/9.8
    = 3.24 or a negative, which we would reject

    it took 3.24 seconds to hit the ground

    c) If you know Calculus ....
    dh/dt = -9.8t + 2 = 0 for a max height
    9.8t = 2
    t = .2041 seconds
    at that time, h = -4.9(.2041^2) + 2(.2041) + 45
    = 45.2041m

    If you don't know Calculus, then you probably learned how to complete the square

    h = -4.9(t^2 -(2/4.9)t +.04165 - .04165) + 45
    = -4.9(t - .2041)^2 + 45.2041
    So the vertex is (.2041 , 45.2041) ---> max is 45.2041

    (same as above)

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