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A small task with Newton's Laws

  1. Jan 1, 2014 #1
    1. The problem statement, all variables and given/known data

    I have been given a small task. There is two parts. (I have translated it from another language):

    "Santa is flying in his sleigh 836,6 feet (250 meters) above the ground. To save time, he will let the packets fall from the sack down the chimney of a house. The package is not broken by this treatment as Santa Claus, knows a top-secret trick. The chimney he must frame is 10 meter (32,8 feet tall.)

    How long does it take the package to drop down the chimney?

    To save the most time a efficiency pixie suggests that Santa must let go of the packages while he is at full speed instead of stopping. Thus he doesn't need to stop at each house.

    Your task now is to help Santa to determine where he will let go of the package, so that it hits its target. Remember to be precise - otherwise there are no gifts for Christmas!

    It is reported that the slide speed is 1200 km / h, and that can be ignored air resistance - this is another one of Santa's hitherto secret tricks.


    2. Relevant equations

    Okay. I know I need to use Newton's Law about gravitation - and I need the accelaration.



    3. The attempt at a solution

    I have an idea about the first task, but i am lost with the second.

    I can find the fall time with this equation:
    h = ½·g·t^2

    Then I just have to isolate for t.

    t^2=h / ½ / g
    t^2 = 240 meter / ½ / 9,82
    t^2 = 48,87
    t = √48,87
    t = 6,99 ≈ 7 seconds
     
  2. jcsd
  3. Jan 1, 2014 #2

    Simon Bridge

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    Welcome to PF;
    if Santa were to drop the presents from directly above the chimney - they would miss! Why?
     
  4. Jan 1, 2014 #3
    Thank you.

    Hey, It made me think about something.

    I guess, you would miss, because the object will fall with a parabolic trajectory in the same direction the plane is flying.

    But ..

    Doesn't the object have the same speed as Santa Claus? in this case 1200 km/hour?

    So now I have the speed of the package and the time it takes to fall down. That means that I can solve this easily with this equation:

    t * v = distance

    So I just have to calculate how far the package will move in 7 seconds, which is 2.3 kilometers. Or am I wrong?

    * I have attached a small graphic

    Screen Shot 2014-01-01 at 08.58.08.png
     
  5. Jan 1, 2014 #4

    ehild

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    It is correct.

    ehild
     
  6. Jan 1, 2014 #5
    Just to make sure.

    How long does it take the package to drop down the chimney?
    - Around 7 seconds.

    Your task now is to help Santa to determine where he will let go of the package, so that it hits its target.
    - 2333.333 meters before the chimney.

    Can one of you confirm that these results are correct?

    And by the way, thank you very much for your help Simon and ehild.
     
  7. Jan 1, 2014 #6

    ehild

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    It is 2333 m before reaching above the chimney. -2333 m before is 2333 m after.:smile:

    ehild
     
  8. Jan 1, 2014 #7

    Oh, the "-" was not written on purpose. But thank you for the heads up! :)

    Have a great day.
     
  9. Jan 1, 2014 #8

    ehild

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    Happy New Year to you!:smile:


    ehild
     
  10. Jan 1, 2014 #9

    Simon Bridge

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    Well done :)
     
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