How Can Relativistic Space Travel Affect Aging and Distance Measurements?

[trans_pie]

1. A 1000m long and 200m wide (when at rest) spaceship equipped with a chronometer is sent on a roundtrip
to their Galactic Base, 8 light years away.
(a) Astronauts start the trip after celebrating their captains 29th birthday and they want to make a round
trip and return to Earth on the eve of the captains 30th birthday. The ship travels with a constant velocity.
Calculate the required speed of the spaceship.
(b) According to the clocks on Earth, how long does this trip take?
(c) At which speed the age difference between the captain of the spaceship and her twin sister staying on
Earth will be minimal when the spaceship returns to Earth?
(d) How large is the distance from Earth to Galactic Base from the ships point of view (when the ship is at
the beginning of its journey but its speed is already equals the minimum speed calculated above)?
(e) Calculate the proper length of the ship when the speed of the ship is 0.5 c relative to Earth.
(f) Calculate the length and the width of the ship in a reference frame where the velocity of the ship is
directed from its tail to head and the speed is 0.5 c.

2. When traveling in space, a ship (length 1000m in its rest frame) passes an identical ship, which is at rest
relative to Earth. The captain of the moving ship decides to measure the speed of her ship. She looks out of
a window and uses her clock to measure the time between the moments when the head and the tail of the
other ship pass. The result of the measurement is 1 ìs. Calculate the speed of the “moving” ship relative to
Earth.

3. Two ships start simultaneously from Earth and move in directions, which are orthogonal to each other and
with equal velocities of 0.8 c. Calculate the distance between the ships as function of time in the rest frame
of one of the ships.

4. Two ships are moving toward each other with velocity of 0.7 c. At time zero in reference frame (reference
frame of Earth), Ship 1 nearly collides with Earth and Ship 2 is at the distance of 105 km from Earth.
(a)How long does it take according to the clock on Earth before the ships collide? What are the coordinates
of each ship at the collision?
(b)The clock in reference frame where Ship 1 is always at origin and at rest is set to zero when Ship 1 nearly
collides with Earth. What will the clock in show when the two ships collide?
(c)Calculate the distance between the two ships in when the Ship nearly collides with Earth.
(d)The distance to the other ship divided by the time until the collision (all measured in the reference frame
of Ship 1) gives the relative velocity of the two ships. Calculate the relative velocity and comment on the
value.

 

[HallsofIvy]

You've listed 4 problems with innumerable "subproblems" and given no indication that you have tried anything on this yourself. Surely you don't expect people to do your homework for you!

 

[Alex6200]

Most of those problems look like straightforward special relativity problems.

 

[Doc Al]

These are all problems in relativistic kinematics, not momentum.

You must show your work to get help. Please review our posting rules, which are linked at the top of every page, and the https://www.physicsforums.com/showthread.php?t=94379".

 

[Alex6200]

If you literally can't make heads or tails of the problems, read this:

http://en.wikipedia.org/wiki/Special_Relativity#Mass.2C_momentum.2C_and_energy

And then just plug in the numbers from the problems. None of those questions seem like curveballs to me, if you understand special relativity you should be able to do them in no time.