1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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!).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook