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Where did the water balloon fall?

  1. Dec 30, 2013 #1
    1. The problem statement, all variables and given/known data
    A boy is on top of a 12 m tall building. He throws a water balloon horizontally, releasing it at a height of 1 m above the top of the building. The water balloon is thrown at 30 mi/h and is aimed at the balconies of an apartment building across the street, 18 m away horizontally. If each story of the apartment building is 3 m high, which balcony gets hit by the water balloon, 1st, 2nd,3rd or 4th floor?

    2. Relevant equations
    t=x/v
    y=y0+v0t1/2 a(t^2)

    3. The attempt at a solution

    I attempted to convert the mi/h to m/s and got 80.3 m/s. I used t=x/v to get my time:

    t=x/v
    t=18/80.3
    t=0.22 s

    The time seems reasonable enough.

    Then I tried using y=y0+v0t+1/2 a(t^2) to find how far down the balloon fell.

    y=y0+v0t+1/2a(t^2)
    1/2 a(t^2)
    y=0+0+1/2 a(t^2)
    y=1/2a(t^2)
    y=1/2(9.8)(0.22^2)
    y=1/2(9.8)(0.0484)
    y=0.24 m

    Something seems off, but I can't place it. If this answer is right, does that mean it will land on the 4th(top) floor of the building?

    Thanks! :smile:
     
  2. jcsd
  3. Dec 30, 2013 #2

    SteamKing

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    Try your conversion of 30 mi/hr to m/s again. 80.3 m/s is a very fast clip.
     
  4. Dec 30, 2013 #3
    Hm, I thought so. 30 mi=48280.3 m. OH, I see. I calculated to m/min. I need to divide by 60 again, correct? So 1.3 m/s.
     
  5. Dec 30, 2013 #4

    SteamKing

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    1.3 m/s is a casual strolling speed. You need to set up your calculations in an organized fashion and not try to 'shoot from the hip'. It's not clear where 80.3 m/s came from originally.
     
  6. Dec 30, 2013 #5
    I didn't think about it that way. Hmm. Okay, so 30 mi/h=48280.3 m/h. Line up the unit conversion so that the hours cancel out. 48280/3600 s=13 m/s. That seems right, finally.
     
  7. Dec 31, 2013 #6
    Is the time right?
     
  8. Jan 27, 2014 #7
    I'm getting 9.3 meters, which would put it at the second (next to bottom) floor. Feel free to confirm or correct the answer! :)
     
  9. Jan 27, 2014 #8

    lightgrav

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    13.4 m/s hits in 1.34s after dropping 8.8m (from 13m start).
    avoid round-offs (especially for things that get squared, like t here), by using the value in the calculator display register.
     
  10. Jan 27, 2014 #9
    Ah, I see. I used 1.38 seconds. Now I'm getting 8.8 as well. So this should put the balloon at the third (from bottom) floor, correct?

    Thanks again!
     
  11. Jan 27, 2014 #10
    This post is only here because I couldn't delete it.
     
    Last edited: Jan 27, 2014
  12. Jan 27, 2014 #11

    lightgrav

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    huh? 13m - 8.8m = ? 1st floor 0 to 3m, 2nd floor 3m to 6m, 3rd floor 6m to 9m, 4th floor 9m to 12m ... right?
     
  13. Jan 27, 2014 #12
    4.2 m. Correct, I don't think I'm thinking about the diagram correctly. It would actually be the second floor, right?
     
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