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Solving for a variable help :)

by MathiasArendru
Tags: solving, variable
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MathiasArendru
#1
Jul31-14, 05:35 PM
P: 12
Hey guys, this is a little silly question but it bothers me. Im not a math genius (yet i hope) and im still in elementary school so theres alot to learn. But i just read about the lorenz factor in this example he basically used pythagoras of this light clock in a train, so it started of as

[tex](ct)^2 = (cx)^2 + (vt)^2[/tex]

and he derived it into:

[tex]t = \frac{x}{\sqrt{1-\frac{v^2}{c^2}}}[/tex]

I would have posted an attemp to solve it but i really just dont know how to crack it and get started

Pleeeaaase help it would be really nice :D
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mfb
#2
Jul31-14, 06:03 PM
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That is nothing you can derive (at least not in the way you ask for here), that is a definition of γ.
MathiasArendru
#3
Jul31-14, 06:18 PM
P: 12
right its me god im stupid! he solved for t not gamma dont really know what went through my head while i wrote it. i corrected it in the post now

micromass
#4
Jul31-14, 06:23 PM
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Solving for a variable help :)

OK, I'll help you get started: bring all terms which have a ##t## to one side of the equation and the other terms on the other side. Isolate ##t^2## so you have ##t^2 = \text{something}##. Then take roots.
MathiasArendru
#5
Jul31-14, 06:35 PM
P: 12
ok ill try:

[itex]c^2t^2 = c^2x^2 + v^2t^2[/itex]
[itex]t^2 = \frac{c^2x^2 + v^2t^2}{c^2}[/itex]
Dividing both sides by t^2
[itex]1 = \frac{c^2x^2 + v^2t^2}{c^2t^2}[/itex]

im stuck... lol
normally i dont really have trouble when solving for variables but this one irritates me.. can i have another hint ? :)
micromass
#6
Jul31-14, 06:47 PM
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Quote Quote by MathiasArendru View Post
ok ill try:

[itex]c^2t^2 = c^2x^2 + v^2t^2[/itex]
[itex]t^2 = \frac{c^2x^2 + v^2t^2}{c^2}[/itex]
I can see a ##t^2## on the LHS and on the RHS. The idea is to have all occurences of ##t^2## on the LHS.
MathiasArendru
#7
Jul31-14, 07:05 PM
P: 12
Exacly thats the though part, because normally i would just divide out the t^2 but that wont help in this example as it would leave me with a 1 on the LHS.. and that wouldnt help much,, is there some mechanism or method that i am missing that could solve this? i feel like theres something i havent learned that could allow this to be solved.. or is it just me thats blind?
micromass
#8
Jul31-14, 07:08 PM
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Quote Quote by MathiasArendru View Post
Exacly thats the though part, because normally i would just divide out the t^2 but that wont help in this example as it would leave me with a 1 on the LHS.. and that wouldnt help much,, is there some mechanism or method that i am missing that could solve this? i feel like theres something i havent learned that could allow this to be solved.. or is it just me thats blind?
If you have ##2x^2 = 5 - 3x^2##, can you solve that? You just need to do the same thing here. Isolate ##x##.
MathiasArendru
#9
Jul31-14, 07:17 PM
P: 12
Yea no problem but there i can just add 3x^2 to both sides, in my example its [itex]v^2t^2[/itex] so i cant do the same thing here?
Nugatory
#10
Jul31-14, 08:04 PM
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Quote Quote by MathiasArendru View Post
Yea no problem but there i can just add 3x^2 to both sides, in my example its [itex]v^2t^2[/itex] so i cant do the same thing here?
You could try subtracting ##v^2t^2## from both sides.
Borek
#11
Aug1-14, 02:33 AM
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Quote Quote by MathiasArendru View Post
Yea no problem but there i can just add 3x^2 to both sides, in my example its [itex]v^2t^2[/itex] so i cant do the same thing here?
Why do you think v2 is different from 3?


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