1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How to show an equation with n'th number of iterations

  1. Apr 2, 2015 #1

    vmr101

    User Avatar
    Gold Member

    1. The problem statement, all variables and given/known data
    An observer measures an object moving away at speed v=0,75, an observer on that object measures another object moving away in the same direction with the same speed relative to it and this is repeated n times. Find the velocity of the n'th object relative to the first.

    I didnt post in the physics section, as its just the maths that is the tricky part. Showing this formula for n objects, when each object relies on the same equation for the previous object etc.


    2. Relevant equations
    w = u+v / (1 + uv) derived from k calculus

    3. The attempt at a solution
    I have understand and have sorted out the physics in this, but am unsure of how to show the answer mathematically. For large n, g => 1.

    g = (a+b) / (1+ab) , where g) is the velocity of the n'th object relative to the original observer.
    b) is the velocity of the last (n'th) object relative to the previous, a) is the previous object velocity relative to the one before it, all the way back to the original.
    In a few steps I keep subbing in this equation into it self, and while I can show it works for small n, It am unsure of how to show this mathematically for large n.
     
  2. jcsd
  3. Apr 2, 2015 #2

    vmr101

    User Avatar
    Gold Member

    I recall something like =(a+b)(1-ab+(ab)^2 - (ab)^3+...
     
  4. Apr 2, 2015 #3

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Look here http://en.wikipedia.org/wiki/Velocity-addition_formula at rapidities. Combining velocities gets complicated. Adding rapidities is easy, they just add. Give an expression using hyperbolic tangents.
     
  5. Apr 4, 2015 #4

    vmr101

    User Avatar
    Gold Member

    I had a look at rapidities but we haven't gone through them so I dont think that's how they want us to show this.
    Any other advice?
     
  6. Apr 4, 2015 #5

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    I guess I don't know any other closed form to express the answer in. Rapidities are easy.
     
  7. Apr 5, 2015 #6

    vmr101

    User Avatar
    Gold Member

    I read up on the rapidities and i can make it work :) Thanks Dick.
     
  8. Apr 5, 2015 #7

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Good for you. I knew you'd like the solution when you figured it out.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: How to show an equation with n'th number of iterations
Loading...