How to Solve the Special Relativity Time Dilation Equation for Velocity

1
How to Solve the Special Relativity Time Dilation
Equation for Velocity

• A Mathematical Puzzle

2
Here is the equation to start with
3
Put in the numbers you want. Note that t0 is the
ship time, and t is the time for the stationary
observer
4
Now, switch the two terms by cross multiplying
15
5
Now, switch the two terms by cross multiplying
15
6
Now, switch the two terms by cross multiplying
15
7
Now, switch the two terms by cross multiplying
8
Now, square both sides
9
Now, square both sides
10
Simplify
11
And convert to a decimal
12
Add to both sides
13
Simplify
14
Simplify
15
Subtract from both sides
16
Simplify
17
Simplify
18
Simplify
19
Take the square root of both sides
20
Take the square root of both sides
21
Cross multiply the c
22
Cross multiply the c
23
Cross multiply the c
24
Cross multiply the c
25
Cross multiply the c
26
You can leave this as your answer
OR
27
Convert to a velocity in m/s