**Examples
for relativity**

Example #1

Problem:

A muon has a
lifetime of 2.2E-8 * s* in its own rest
frame. If it travels with a speed of 0.95c, how far will it
travel before it decays?

Solution:

The distance if * vt*,
but the time is longer by a factor

20.1
*m*

Example #2

Problem:

A meter stick
flies by with an apparent length of 60 *cm*. What is its
velocity?

Solution:

Starting with **g **equal to (1/0.6), solve for * v*.

* v*
= 0.8c = 2.4E8

Example #3

Problem:

Two space ships approach each other with velocities of 0.9c. According to an observer on the space ship, what is the velocity of the other ship.

Solution:

Use the velocity addition formula,
.
Both * u* and

* v'*
= 0.9944c

Example #4

Problem:

a.) Two space ships travel in the same direction, with one travelling at 0.9c, the other travelling at 0.99c. What is the velocity of the faster ship according to an observer on the slower ship.

Solution:

Again use the velocity addition
formula, with **u ***= *0.99c and **v****
**= **- **0.9c.

* v'*
= 0.825c

b.) What is the velocity of the slower ship according to an observer on the faster ship?

* v'*
= -0.825c

Example #5

Problem:

A proton and an antiproton approach each other moving with a velocity of 0.999c. They fuse to form a new particle. What is the mass of the created particle?

Solution:

The energy of each proton is **m**_{0}**g****c**^{2}. Multiplying it by two and dividing by **c**^{2
}gives the new
particle's mass.

* m*
= 7.5E-26