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Help with mental blank





Bikerman
A couple of years ago I wrote an intro to Special Relativity. I've just dug it out with a view to polishing it up and sticking it on my website.
In the paper I show how the time dilation factor can be derived simple, using nothing more than Pythagoras. Trouble is, I've forgotten how I managed one of the steps in the simplification - complete mental blank.
A copy of my working is below - how did I go from 4 to 5? Anyone?
(How embarrassing....Sad )
kelseymh
Bikerman wrote:
A couple of years ago I wrote an intro to Special Relativity. I've just dug it out with a view to polishing it up and sticking it on my website.
In the paper I show how the time dilation factor can be derived simple, using nothing more than Pythagoras. Trouble is, I've forgotten how I managed one of the steps in the simplification - complete mental blank.
A copy of my working is below - how did I go from 4 to 5? Anyone?
(How embarrassing....Sad )


Square both sides of (4) and split the ratio to obtain,

t0^2 = (D/c)^2 + (v/c)^2 t0^2

Then collect the t0 terms,

t0^2 (1 - (v/c)^2) = (D/c)^2

Divide and take the square root,

t0 = (D/c) / sqrt(1 - (v/c)^2)
Bikerman
Thanks Mike - now you say it I see it immediately - but I had a complete blank until then Smile
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