SOLUTION: I was asked to solve for (v) in terms of the other variables. Please help? T= To/sqrt(1-v^2/c) If you know the solution please explain. I was told this was Einstein's speci

Algebra ->  Radicals -> SOLUTION: I was asked to solve for (v) in terms of the other variables. Please help? T= To/sqrt(1-v^2/c) If you know the solution please explain. I was told this was Einstein's speci      Log On


   

Question 27418: I was asked to solve for (v) in terms of the other variables. Please help?
T= To/sqrt(1-v^2/c)
If you know the solution please explain. I was told this was Einstein's special theory of relativity
T= starship = 8 hrs (passed)
To= me on Earth = 4 hrs (passed)
c= the speed of light =186,000 miles per second
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
you mis-quoted the formula... it is T=+To%2Fsqrt%281-%28v%2Fc%29%5E2%29

Re-arranging, first get rid of the square root by squaring both sides, giving

T%5E2+=+To%5E2%2F%281-%28v%2Fc%29%5E2%29
1-%28v%2Fc%29%5E2+=+%28To%5E2%29%2F%28T%5E2%29
1+-+%28%28To%5E2%29%2F%28T%5E2%29%29+=+%28v%2Fc%29%5E2
sqrt%281+-+%28%28To%5E2%29%2F%28T%5E2%29%29%29+=+v%2Fc
c%2Asqrt%281+-+%28%28To%5E2%29%2F%28T%5E2%29%29%29+=+v

Now, this is an answer. You could also mess with the square root term and combine the 1 to the fraction. Ultimately you will get:

v+=+%28c%2Asqrt%28%28T-To%29%28T%2BTo%29%29%29%2FT+

So,
T = 8 hrs
To = 4 hrs
c = 186,000 miles per second

First thing... convert all terms to consistent units: you have times in hours yet your speed of light is miles per SECOND.

I shall convert the speed to miles per hour:

186,000 miles EVERY second is
186,000*60 miles EVERY minute ---> you will go further in a minute than a second
186,000*60*60 miles EVERY hour ---> you will go further in an hour than a minute

So, put the numbers into the formula, giving: v=c%2Asqrt%281+-+%28%28To%5E2%29%2F%28T%5E2%29%29%29
v=%2818600%2A60%2A60%29%2Asqrt%281+-+%28%284%5E2%29%2F%288%5E2%29%29%29
v=%2818600%2A3600%29%2Asqrt%281+-+%28%2816%29%2F%2864%29%29%29
v=%2818600%2A3600%29%2Asqrt%281+-+%281%2F4%29%29+
v=%2818600%2A3600%29%2Asqrt%283%2F4%29+

now use a calculator... v = 3350 miles per hour

jon.