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Homework Help: Horizontal distance homework

  1. Nov 23, 2007 #1
    [SOLVED] a question

    a railcart moves along a railway at constant velocity [tex]v_0[/tex] with a ball attached to its ceiling. at t=0 the ball is drooped from the ceiling and at the same time the railcart breaks are pushed creating deceleration such that its velocity is:
    [tex]v=v_0e^{ -pt}\hat{x}[/tex] .
    h is the distance between the ceiling and the floor.
    in which horizontal distance will the ball hit the floor of the railcart. given [tex]v_0[/tex]=70m/sec
    h=180m p=0.0185 1/sec g=10m/sec^2
    if you can help me understand this and solve it
    thanks
     
    Last edited: Nov 23, 2007
  2. jcsd
  3. Nov 23, 2007 #2

    Dick

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    You will have to integrate the x velocity dt to get the horizontal displacement as a function of time. The vertical displacement is the usual (1/2)*g*t^2. Use that to find t when it hits the floor and put it into the x displacement.
     
  4. Nov 23, 2007 #3
    clarifications

    ok i understood
    but when i integrate i have an [tex]x_0[/tex] is it zero or because the railcart is decelerating i need to find it.
    and another question regarding the use of the well known equation [tex]x=v_0t+ \frac{at^2}{2}[/tex] since there is an acceleration shoulnt there be a different accelaration according to the galilean transformation in accelerated systems
     
  5. Nov 24, 2007 #4
    ok i did as you told me and got after integrating [tex]\frac{v_0e^{-pt}}{-p}[/tex] and the answer wasnt right. i got -3386.25m fot the time 6sec
    i think it has to do with the fact that i didnt calculate the [tex]x_0[/tex] how do i do that
     
    Last edited: Nov 24, 2007
  6. Nov 24, 2007 #5

    Dick

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    Your problem is that you can't just plug t=6 into that. You have to put t=6 and t=0 and then subtract them. It's an indefinite integral.
     
  7. Nov 24, 2007 #6

    Dick

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    There is no 'x0' to find. The initial value of x doesn't matter. This is all about differences. And there is no need to change frames. You are doing fine solving the problem is this one.
     
  8. Nov 24, 2007 #7
    **** i dont believe it i made that stupid mistake of not putting a zero in the integral

    dude thak you very much
    your the best
    keep on helping it is the nicest thing ever
     
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