Solving for a variable help

1. MathiasArendru

15
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

$$(ct)^2 = (cx)^2 + (vt)^2$$

and he derived it into:

$$t = \frac{x}{\sqrt{1-\frac{v^2}{c^2}}}$$

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

Last edited: Jul 31, 2014

Staff: Mentor

That is nothing you can derive (at least not in the way you ask for here), that is a definition of γ.

3. MathiasArendru

15
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

4. micromass

18,932
Staff Emeritus
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.

5. MathiasArendru

15
ok ill try:

$c^2t^2 = c^2x^2 + v^2t^2$
$t^2 = \frac{c^2x^2 + v^2t^2}{c^2}$
Dividing both sides by t^2
$1 = \frac{c^2x^2 + v^2t^2}{c^2t^2}$

im stuck... lol
normally i dont really have trouble when solving for variables but this one irritates me.. can i have another hint ? :)

6. micromass

18,932
Staff Emeritus
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.

7. MathiasArendru

15
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?

8. micromass

18,932
Staff Emeritus
If you have ##2x^2 = 5 - 3x^2##, can you solve that? You just need to do the same thing here. Isolate ##x##.

9. MathiasArendru

15
Yea no problem but there i can just add 3x^2 to both sides, in my example its $v^2t^2$ so i cant do the same thing here?

Staff: Mentor

You could try subtracting ##v^2t^2## from both sides.

Staff: Mentor

Why do you think v2 is different from 3?