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1-d kinematic problem

  1. Oct 4, 2007 #1
    1. The problem statement, all variables and given/known data
    A canonball is launched up in the air with velocity v_0. There is air resistance, which is equal to kmv (where k is some proportionality constant and m is the mass of the canonball) and is proportional to the canonball's velocity. How long does it take to reach its maximum height.

    2. Relevant equations

    3. The attempt at a solution

    I got t=ln(g)/k as the time. I would just like to verify if that is the correct solution. g=earth's gravitational acceleration constant.
  2. jcsd
  3. Oct 4, 2007 #2


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    Your answer is incorrect. Perhaps if you showed your working we could point you in the right direction...
  4. Oct 4, 2007 #3
    i realize that my units are off by a lot. i realized that i get the total acceleration to be
    -kv+g=(dv)/(dt), but when i try and integrate it by (dv)/(-kv+g)=dt i get incorrect units. is the g supposed to stay on the other side of the equation. If so how can I integrate it? and after that I am not quite sure about how to use v_0 given to me?
  5. Oct 4, 2007 #4
    i would like to verify if this is correct. I checked to make sure if it is in the right units.

    t=-ln[(v_0/g)k +1]/k
  6. Oct 4, 2007 #5


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    I'm getting exactly the same thing but without the minus sign.

    I think the minus sign shouldn't be there because ln(positivenumber + 1) > 0... so with that minus sign there you'll get a negative time.
  7. Oct 4, 2007 #6
    i got it in terms of my integration bounds for the integral with dv. i set the bounds from v to 0
  8. Oct 4, 2007 #7


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    should you be using -kv - g... or are you using g = -9.8 instead of g = 9.8?
  9. Oct 4, 2007 #8
    i see i was doing it wrong the whole time
  10. Oct 4, 2007 #9
    i accidentally made the force in my free body diagram like this:


    i thought that since the acceleration was negative with respect to my reference frame, the -a was necessary when the right hand side of the equation took care of that.
    thanks for your help.
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