Post on 22-Apr-2015
description
How to Solve the Special Relativity Time Dilation
Equation for VelocityA Mathematical Puzzle
2
2
0
1cv
tt
Here is the equation to start with
2
2
1
1215
cv
Put in the numbers you want. Note that t0 is the ship time, and t is the time for the stationary observer
12
Now, switch the two terms by cross multiplying
2
2
1c
v
15
12
2
2
1c
v
15
Now, switch the two terms by cross multiplying
12
2
2
1c
v15
Now, switch the two terms by cross multiplying
15
122
2
1c
v
Now, switch the two terms by cross multiplying
Now, square both sides
15
122
2
1c
v
Now, square both sides
2
15
12
2
2
2
1
c
v
Simplify
225
1442
2
1c
v
And convert to a decimal
64.02
2
1c
v
Add to both sides
2
2
64.0c
v2
2
2
2
1c
v
c
v
Simplify
2
2
64.0c
v2
2
2
2
1c
v
c
v
Simplify
2
2
64.0c
v1
Subtract from both sides
2
2
64.064.0c
v64.01
Simplify
2
2
64.064.0c
v64.01
Simplify
2
2
c
v64.01
Simplify
2
2
c
v36.0
Take the square root of both sides
2
2
c
v36.0
Take the square root of both sides
c
v60.0
Cross multiply the c
c
v60.0
Cross multiply the c
v60.0 c
Cross multiply the c
v60.0c
Cross multiply the c
v60.0 c
Cross multiply the c
v60.0 c
You can leave this as your answer
v c60.0
OR
Convert to a velocity in m/s
v )100.3(60.0 8
s
m
s
m8108.1