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Motion of the skydiver

  1. Mar 4, 2007 #1
    1. The problem statement, all variables and given/known data

    A skydiver makes a controlled descent from an aeroplane to the ground. He
    undergoes a number of seconds of freefall at his terminal speed before opening
    his parachute, after which he decelerates to a new terminal speed. He continues to
    fall at this speed for some time before landing on the ground.
    Describe the motion of the skydiver starting from the moment he leaves the
    aeroplane and finishing shortly before he hits the ground. You should divide the
    descent into a number of phases. For each phase identify the vertical forces acting
    upon the skydiver, and describe his motion using Newton’s laws. Where it is
    useful to do so, as an approximation, you may treat the skydiver as behaving like
    a sphere during his descent.
    Remember to define the frame of reference that
    you are using to describe the motion. You may ignore any horizontal forces and
    motions.
    As much detail answer preferable.


    2. Relevant equations

    F=MA
    newtons laws


    3. The attempt at a solution

    minimum speed at start, increasing speed as time passes by. Until he hits the ground, where this is max speed. Vertical force going downwards increases as time goes by and upward vertical force decreases.



    [answer so far=

    phase A= skydiver jumps out of plane traveling at speed till reaches terminal velocity
    phase B = opens parachute , skydiver decelaretes to new terminal velocity
    phase C= skydiver continues at this speed till reaches ground

    phase A: person jumps out, accelerates until reaches termainal velocity, then a = o.

    Person opens chute...
    Right after the chute is opened, acceleration up

    phase B: drag and air resistance are the same. The chute changes the profile of the falling object. The shape of the object changes, so the drag force will change as well.

    During the entire fall, there are only two vertical forces, gravity and the drag force. The drag depends upon several aspects of the falling object.

    phase A:
    downward force- gravity,
    upward force- air resistance

    phase B:
    downward force-gravity
    upwward force= drag and air resistance

    phase C:
    downward force=gravity
    upward force=no upward force when reached ground


    ?is this all ok?]
     
    Last edited: Mar 5, 2007
  2. jcsd
  3. Mar 4, 2007 #2

    Hootenanny

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    Staff Emeritus
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    Gold Member

    For simplicity, let us just consider the vertical motion and speed. Are you sure that his speed continues increasing until he hits the ground? Are you also sure about your analysis of the forces involves? What does the term terminal velocity mean to you?
     
  4. Mar 4, 2007 #3
    terminal velocity= maximum velocity, so therefore his speed reachese a limit while he is sky diving, at is at constant speed during some time before he reaches the ground.
    This is to say acceleation will be constant when speed reaches max velocity.
    So at that time vertical motion upward and downward will be equal.

    ??is this correct...any more details i can add
     
  5. Mar 4, 2007 #4

    hage567

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    Homework Helper

    "This is to say acceleation will be constant when speed reaches max velocity."

    Are you sure about this? If his velocity is not increasing, how can he still be accelerating?
     
  6. Mar 4, 2007 #5
    after speed reaches maximum veloity speed will remain contstant therefore...no accelration.
     
  7. Mar 4, 2007 #6

    hage567

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    Homework Helper

    That's correct.
     
  8. Mar 4, 2007 #7
    thanks Hage567...

    well nearly there......just need to complete it.

    Describe the motion of the skydiver starting from the moment he leaves the
    aeroplane and finishing shortly before he hits the ground.

    [i think this is kinda done]

    You should divide the descent into a number of phases. For each phase identify the vertical forces acting upon the skydiver, and describe his motion using Newton’s laws. Where it is useful to do so, as an approximation, you may treat the skydiver as behaving like a sphere during his descent.

    [still need to do]
     
  9. Mar 4, 2007 #8
    Dividing the descent into a number of phases.

    phase A= leaves the plane till reaches max velocity
    phase B= terminal velocity till just hits the ground

    any more phases that can be added?
     
  10. Mar 4, 2007 #9
    What about the parachute opening?
     
  11. Mar 4, 2007 #10
    what about it? please tell me more phases -well
    would phase A be parachute opehing?

    phase A = be parachute opehing
    phase B= leaves the plane till reaches max velocity
    phase C= terminal velocity till just hits the ground

    is this corect?
     
  12. Mar 4, 2007 #11
    The problem states that the person falls at a constant velocity for a few seconds before opening the chute. So it looks like you need a "phase" before your stated phase A.
     
  13. Mar 4, 2007 #12
    phase A= skydiver jumps out of plane traveling at speed till reaches terminal velocity

    phase B = opens parachute , skydiver decelaretes to new terminal velocity
    phase C= skydiver continues at this speed till reaches ground

    any more phases that could be added?
     
  14. Mar 4, 2007 #13
    I think phase A can be broken down further.
     
  15. Mar 4, 2007 #14
    For each phase identify the vertical forces acting upon the skydiver-

    phase A:
    downward force- gravity,
    upward force- air resistance

    phase B:
    downward force-gravity
    upwward force=thrust and air resistance

    phase C:
    downward force=gravity
    upward force=no upward force when reached ground

    are these vertical forces correct?
     
  16. Mar 4, 2007 #15
    Phase B- thrust is an unusual term here, what do you mean.
    Also, did you take this into account for your description of phase A/phase B: the person jumps out, reaches terminal velocity, falls at this rate for a few s, then opens the chute.
     
  17. Mar 4, 2007 #16
    thrust its a guess...
     
  18. Mar 4, 2007 #17
    What changes when the person opens the chute?
     
  19. Mar 4, 2007 #18
    speed increases going upwards,
    upward force increases more then downward force.
     
  20. Mar 4, 2007 #19
    So what you are saying is that just after the chute opens, the person starts moving faster? does that make sense?

    speed is a scalar
     
  21. Mar 4, 2007 #20
    As the velocity vector becomes more downward, the drag force starts to act more and more in the upward direction, the skydiver continues to accelerate downward (but does not accelerate downward quite as quickly as -g). As the skydiver approaches the terminal velocity, the net force becomes smaller and smaller (and the divers motion becomes almost uniform).
     
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