How Do I Isolate Velocity in the Lorentz Factor Equation?

[phys121]

Alright, I am not the best at algebra. So i was wondering if anyone could show me how to get the V out on its own in the lorentz factor equation

l= 1/\sqrt{1-(v^2/c^2)}


I tried to first times both sides by bottom then manipulate it but i just can't get it right.

Any help would be much appreciated!

 

[Doc Al]

Not exactly sure what you're trying to accomplish, but you can take:
γ = 1/√(1 - v²/c²)

and solve for v in terms of γ.

Cross-multiply and then square both sides.

 

[phys121]

What, you mean like this...

\gamma(\sqrt{1-v^2/c^2})=1

then: finally finishing with;

\sqrt{(1-1^2/\gamma^2)c^2}=v

??

 

[icystrike]

What, you mean like this...

\gamma(\sqrt{1-v^2/c^2})=1

then: finally finishing with;

\sqrt{(1-1^2/\gamma^2)c^2}=v

??

your question was 1/\sqrt{1-v^2/c^2}=1 ?

 

[phys121]

My question is how do i solve for "v", that l should be an L lower case. as in lorentz factor "L". not a 1. sorry

Like what should the final equation be?

 

[icystrike]

What, you mean like this...

\sqrt{(1-1^2/\gamma^2)c^2}=v

??

this is wrong.
return to the previous step square both sides, you don't have to multiply gamma into the square root.

 

[phys121]

ah, right i get you now. Thanks!