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Sandbag Dropped from Moving Balloon

  1. Oct 12, 2012 #1
    1. The problem statement, all variables and given/known data
    Hey guys, I'm struggling on the following question:

    Consider a hot air balloon travelling upwards at a constant speed of 10 m/s. A passenger drops a small sandbag over the side of the balloon when the balloon was 40 m above the ground. For how long does the sandbag stay in the air before falling to the ground?
    Known:
    a=-9.81 m/s2
    x0=40 m
    x1=0 m
    v0=0 m/s
    v1=?
    t=?

    2. Relevant equations
    v1=x0+v0Δt+0.5aΔt2

    3. The attempt at a solution
    0=40+0.5(-9.8)Δt2
    -40=-4.9Δt2
    8.16=Δt2
    Δt2=±2.86

    Since time cannot be negative, it takes 2.86 seconds, is this correct? Thanks in advance.
     
  2. jcsd
  3. Oct 12, 2012 #2
    Since the balloon is moving upwards and the sandbag was dropped from the balloon, the initial velocity of the sandbag is the same as the velocity of the balloon. Other than that, you did everything right.
     
  4. Oct 12, 2012 #3
    So from there you use the quadratic formula to solve for t, then again omit the negative answer? Thank you!!
     
  5. Oct 12, 2012 #4
    correct
     
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