GR8677 #69



Alternate Solutions 
casseverhart13 20190829 02:53:50  Merely a smiling visitant here to share this problem! tree trimming   ben 20060719 15:54:53  i think an easier way to do it that gives the exact answer without having to memorize a table is to simply solve for v explicitly in the equation 3/sqrt(1v^2/c^2)=5. just square both sides and you'll find that v^2/c^2=16/25 at which point the answer is obvious.  

Comments 
casseverhart13 20190829 02:53:50  Merely a smiling visitant here to share this problem! tree trimming   RusFortunat 20151021 16:04:12  Just a little typo. At last string you have $\\beta >0.75c\\beta >0.75$   wittensdog 20091007 16:20:35  I've found a way that works for me for remembering how to get the velocity when the lorentz factor is known. If b is the velocity in units of c, aka, v/c, and g is the lorentz factor, then we have,
g = [ 1  b^+2] ^  (1/2)
b = [ 1  g^2 ] ^ +(1/2)
after working through the math. The way that I remember it is that if you take one of them, swap b and g, and then swap the exponent signs, you get the other one. So they have some kind of nice antisymmetry, or whatever you want to call it.
Hope this helps someone...   barefoot0 20061127 12:23:00  But 16/25 is .64 not .8 so you would get answer B instead. But ETS said answer C is correct.
barefoot0 20061127 12:25:13 
never mind I forgot to take the square root.

  nitin 20061121 04:19:22  trombone,
I think you need to check yourself out. You're acting like a kid, and your aim is clearly to insult me, which is a shame since I did not address you in anyway. Your attitude is that of a moron, and Lubos Motl has given a good definition of it.   nitin 20061116 11:25:38  Another nonsensical solution...
Ben is right, and I simply don't understand why you decide to change from the fractional form "" to the decimal form "", which drives you into a long mess!
trombone 20061118 19:16:45 
The only nonsensical thing here is you bitching about the method that was used. Post a better solution if you have one, otherwise stop whining.

  tera 20060813 07:38:59  The comment of ben is quite correct iti isd very simply because the square roots become precise
  ben 20060719 15:54:53  i think an easier way to do it that gives the exact answer without having to memorize a table is to simply solve for v explicitly in the equation 3/sqrt(1v^2/c^2)=5. just square both sides and you'll find that v^2/c^2=16/25 at which point the answer is obvious.
Goddar 20091004 23:13:11 
Same here, i find it very useful on this type of question to express gamma as a fraction:
=
Then in units of c:
v =
Saves precious time.

shak 20100731 21:27:32 
that is the easiest way! i dont understand why Yosun approached this problem in a very complicated way

neon37 20101103 12:07:17 
Goddar, thats a neat trick. Saves few precious seconds! It's simplicity makes me say... why didnt I think of that!

 

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