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Kinematics: Average Deceleration Underwater

  1. Jan 26, 2008 #1
    [SOLVED] Kinematics: Average Deceleration Underwater

    Hello! First poster here. :cool: Here is a tough question from my online HW:

    1. The problem statement, all variables and given/known data
    A person jumps off a diving board 5.0 m above the water's surface into a deep pool. The person’s downward motion stops 1.6 m below the surface of the water. Estimate the average deceleration (magnitude) of the person while under the water.

    Answer: _blank_ m/s^2.

    2. Relevant equations
    V^2=Vo^2-2gy
    V^2=Vo^2+2a(x-xo)
    Vf=0

    3. The attempt at a solution
    I asked my physics professor for assistance and tried the problem on my own but came to no avail. I started off by using the first V squared formula and plugging in the known variables to find the velocity of the person as they approach the surface of the water.

    Then, I plugged the inital velocity into the 2nd V squared equation, as this is the velocity as the person struck the water, and still couldn't find the correct answer. I must be having an algebraic issue.

    Okay, there are two distances: 5 m above the water and 1.6 m below the surface of the water. So there is a combined total of 6.6 meters traveled. For above the water:

    Vo or inital velocity is zero.

    V^2=Vo^2-2gy
    V^2=-2gy
    V^2=-2(9.8m/s^2)(5m)
    V^2=-98m/s

    Then take the absolute value of the the square root?

    |V|=Sqroot(98m/s)
    V=9.8895 m/s

    Now, use the second equation to find out the deceleration under the water:

    Xo equals zero.
    Vf or final velocity is zero.

    V^2=Vo^2+2a(X-Xo)
    (Plug in inital velocity when the person struck the water and underwater distance for X.)
    V^2=(9.8995m/s)^2+2a(1.6m)
    V^2=98 m^2/s^2 + (3.2m)a
    (Plug in zero for final velocity and move a to the other side)
    a=98 m^2/s^2 + 3.2m

    Then....? Im not sure. :confused: Any help would be great. Thank you! :smile:
     
    Last edited: Jan 26, 2008
  2. jcsd
  3. Jan 26, 2008 #2

    PhanthomJay

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    Welcome aboard! Check your algebra. You have 0 = 98 + 3.2a. You've got to subtract 98 from both sides before you solve for a.
     
  4. Jan 26, 2008 #3
    Thank you! That worked. I knew I had a fault somewhere in my Algebra. :cool:
     
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