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