**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:

How much is the diameter of the Earth reduced due to the motion of the Earth around the sun.

DATA: *R*_{earth_orbit}=1.5E10
*m*, *D*_{earth}=1.28E7 *m*

Solution:

Calculate the Earth's velocity, using the circumference of
the orbit and the length of a year in seconds. Then calculate the g factor. The earth is shorter by an
amount *D(**1-1/g).*

** v **=
2990

Example #4

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 #5

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'*
= 0.825c

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

* v'*
= -0.825c

Example #6

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 _{p} *

* m*
= 7.5E-26