1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: How to derive the velocity addition formula

  1. Oct 1, 2012 #1
    1. The problem statement, all variables and given/known data
    Derive the formula v= (v'+u)/(1+v'u/c^2) the velcoty addition formula using the below formulas?

    2. Relevant equations
    1. vt1=L+ut1
    2. (proper time)=(proper length)/v'+(proper length)/c
    3. ct2=L-ut2
    4. (dilated time)= (proper time)/(sqrt(1-v^2/c^2))
    5. L=(proper length)sqrt(1-v^2/c^2)

    3. The attempt at a solution
    Ok so here is what I did I solved equation 1 above for t1 and got t1=(L+ut1)/v and equation 3 for t2 and got t2=(L-ut2)/c. I then added them together to get (dilated time or delta t)=(L+ut1)/v+(L-ut2)/c. Then I used equation 4 to get ((L+ut1)/v+(L-ut2)/c)sqrt(1-v^2/c^2)=(proper time). Then I set that equal ti equation 2 ((L+ut1)/v+(L-ut2)/c)sqrt(1-v^2/c^2)= (proper length)/v'+(proper length)/c. Then (proper length)=L/sqrt(1-v^2/c^2) and this is where I get lost in my algebra I cant seem to get rid of L and (proper length) in order to find the correct formula?
  2. jcsd
  3. Oct 1, 2012 #2
    whoops I think I caught some of my errors when I solved for t1 and t2 I forgot the other side?
  4. Oct 1, 2012 #3
    ok after reworking a bit I am still lost but 1 step closer I think. (Proper length)/v'+(proper length)/c=sqrt(1-v^2/c^2)(L/(c+u)+L/(v-u)) I have then tried using the length contraction on this but it gets very complicated uggg.
  5. Oct 2, 2012 #4
    Is it too confusing, should I resubmit
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook