This document provides step-by-step instructions for solving the special relativity time dilation equation to determine the velocity of an object, starting with the basic time dilation equation and demonstrating the mathematical steps of cross multiplying, squaring both sides, simplifying, and taking square roots to isolate the velocity variable.

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. 15 Now, switch the two terms by cross multiplying

6. 15 Now, switch the two terms by cross multiplying

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