## Galilean Velocity Addition and Time dilation

For each problem, include a couple of sentences to briefly describe what you are doing,

even if your answer is mathematical. This will help us understand your work and

allocate partial credit.

You can use a calculator, but please show your work.

1. Galilean Velocity Addition: consider a stationary observer watching a train

moving to the right at a constant velocity of 30 meters per second. (Note: this problem

concerns movement in one direction, along a straight train track, and refers to the two

possible directions as left and right.) Assuming Galilean relativity, how fast are the

following objects moving as measured by the stationary observer, and in what direction

(left or right)?

(a) someone running in the train to the right at a speed of 5 meters per second relative

to the train

(b) someone running in the train to the left at a speed of 5 meters per second relative

to the train

(c) James Bond riding a motorcycle within the train to the left at a speed of 30 meters

per second relative to the train (the Core office requests that I tell you not to try this)

(d) a light beam moving to the left in the train (for this part and part (e) use the exact

value of the speed of light, which is defined to be c = 299,792,458 m/s, and assume

this velocity is relative to the train)

(e) a light beam moving to the right in the train

2. Velocity Addition in Special Relativity: repeat problem (1) using special relativity,

instead of Galilean relativity. For parts (a) through (c) you can round c to 3 x 108 m/s,

and you can round your answers to show 1 digit after the decimal place. For parts (d)

and (e) you should use the exact value of the speed of light. Comment on how your

answers compare to your answers for problem (1).

3. Time Dilation: neutrons have a lifetime of about 15 minutes. Physicists routinely

produce neutrons with high velocities in particle colliders. What is the lifetime of a

neutron, measured by a stationary observer, in the following states of motion:

(a) at rest

(b) traveling with velocity: 0.1 x c

(c) traveling with velocity: 0.9 x c

(d) traveling with velocity: 0.999 x c