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Velocity, time, acceleration etc

  1. Feb 9, 2009 #1
    1. The problem statement, all variables and given/known data

    A hot air balloon is ascending at the rate of 13 m/s and is 93 m above the ground when a package is dropped over the side. How long does the package take to reach the ground? With what speed does it hit the ground?

    2. Relevant equations

    x(t)= initial position + final velocity * time

    v(t)= (acceleration * time) + initial velocity

    x(t)= .5 * (acceleration * (time^2)) + (initial velocity * time) + inital position

    x= initial position * (average velocity * time)

    average velocity= (final velocity - initial velocity) / (2)

    (final velocity^2) - (initial velocity^2) = 2 * acceleration * change in position


    3. The attempt at a solution

    I manipulated equation 4 to solve for time and got 7.15 s, which is wrong. Then I began thinking "Do I need to double this time?" Is it supposed to be 14.31 s?
    For question 2, I used the last equation to solve for final velocity and got 50.86 m/s which it also marked incorrectly. Can anyone please explain this to me? I seem to be having trouble with motion in two direction thing...
     
  2. jcsd
  3. Feb 9, 2009 #2

    LowlyPion

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    It's only motion in one dimension. You just need to set up your equation.

    Use:

    x = Xo + Vo*t - 1/2*g*t2

    Xo is your initial height. Vo is your velocity (+ is up)

    The third term is -, as g is down.
     
  4. Feb 9, 2009 #3
    I'm solving for time. I don't know how to manipulate that equation to get time by itself. Is there another one on here I can use?
     
  5. Feb 10, 2009 #4

    LowlyPion

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