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Homework Help: Balloon problem

  1. Sep 22, 2012 #1
    1. The problem statement, all variables and given/known data
    Question: A hot-air balloon is ascending at the rate of 12m/s and is 80m above the ground when a package is dropped over the side.
    a.)How long does the package take to reach the ground? b.)With what speed does it hit the ground?

    2. Relevant equations
    I know -- acceleration = -9.8 Initial velocity = 12 m/s and initial height = 80 m.

    I know I have to use this formula
    Xf = Vo + 1/2 (g) (T)2

    Vo = 12 m/s
    Xf = 80 m
    g = -9.8 m/s2

    I set Xf to 0.

    How would I find Time?

  2. jcsd
  3. Sep 22, 2012 #2

    Doc Al

    User Avatar

    Staff: Mentor

    I think you mean:
    Xf = Xo + Vo(T) - 1/2 (g) (T)2
    where g = 9.8 m/s2
    Time is the only unknown in the above quadratic equation, so solve for T.
  4. Sep 23, 2012 #3
    How would I go on about doing that? I cant seem to get T by itself in this equation.
  5. Sep 23, 2012 #4
    That user is correct by the way because this is the form you should get. Well, since the object starts 80 m above the ground, x_0 = 80 obviously.

    Here is the equation you get:

    x_f = 80 + 12t - 4.9t²

    It's not impossible to find t. To find t, use the quadratic equation as that user indicates. That is the way to find t. Remember that:

    at² + bt + c = 0 OR c + bt + at² = 0

    t = (-b ± √(b² - 4ac))/(2a)


    t = (-b + √(b² - 4ac))/(2a) or t = (-b - √(b² - 4ac))/(2a)

    By letting the corresponding values be the a, b, c variables and then, solving for t, you should get the answer (it must be positive!).
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