# HW 35-36

Each figure below shows a spaceship moving past your spaceship ("YOU") at the indicated speed. Imagine that you watch the other spaceship as its clock ticks off one second. Rank the figures according to how much time you would say passes (on your own ship) while the other ship's clock ticks off one second, from the shortest to the longest amount of time.
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Each figure below shows a spaceship moving past your spaceship ("YOU") at the indicated speed. Imagine that you watch the other spaceship as its clock ticks off one second. Rank the figures according to how much time you would say passes (on your own ship) while the other ship's clock ticks off one second, from the shortest to the longest amount of time.
The four figures below are the same as those in Part A. This time, imagine that the passengers on the other spaceship are watching your clock as its ticks off one second. Rank the figures according to how much time the passengers (on the other ship) would say passes (on their ship) while they watch your clock tick off one second, from the shortest to the longest amount of time.
Shortest: speed = 0.7c
speed = 0.75c
speed = 0.8c
Longest: speed = 0.85c

The passengers on the other ship must observe the same effects on you as you observe on them, because both of you are in free-float reference frames and there is no way to say who is "really" moving. In other words, just as you say time is running slow on their ship, they say time is running slow on your ship. That is why the answer here is the same as the answer in Part A.
You would observe that the passenger in the other spaceship has a slower heart rate than you do, and she would observe that you have a slower heart rate than hers.

Strange as it may sound, you will claim that time is running slow on her spaceship while she will claim that time is running slow on your spaceship. This is an example of what Einstein told us when he discovered that measurements of time and space are relative.
Each figure below shows a spaceship moving past your spaceship ("YOU") at the indicated speed. Assume that all the spaceships have equal length when at rest and that you watch the other spaceship as its clock ticks off one second. Rank the figures based on the length that you would measure for the other spaceship (in its direction of motion), from shortest to longest.
shortest: speed = 0.85c
speed = 0.8c
speed = 0.75c
longest: speed = 0.7c

The passenger on the other ship must observe the same effects on you as you observe on her, because both of you are in free-float reference frames and there is no way to say who is "really" moving. In other words, just as you say that her ship is contracted in length, she says that your ship is contracted in length. That is why the answer here is the same as the answer in Part A.
We can summarize the results of Parts A and B as follows: When another spaceship is moving by you (at constant velocity), you will measure the spaceship to be shorter than its rest length, while passengers on that ship will measure your length to be shorter. Imagine that you and the passengers on the other ship are arguing (by radio) about who really is the one that has become shorter. To settle the argument, you agree to meet up on Mars and put the two spaceships next to each other to see which one is really shorter. What will you find when you meet up on Mars?
Both spaceships are the same length.

Once you put the two spaceships next to one another, you are in the same reference frame and therefore everyone will agree that the two ships have the same length. The lengths differ only when the ships are moving relative to each other, and of course you cannot compare the ships next to one another while they are moving.
Larger/longer than rest value
-one second on your clock as seen by spaceship passengers-one second on a spaceship clock as seen by you-mass of spaceship as measured by you-your mass as measured by spaceship passengers

Smaller/shorter than rest value
-distance to Vega as measured by spaceship passengers-length (in the direction of motion) of the spaceship as measured by you

Same as rest value
-speed of the spaceship's headlight as measured by you
Consider the following five statements:
1. The green light and red light both flash at the same time.
2. The green light reaches Jackie before the red light reaches her.
3. The green light and red light reach you at the same time.
4. Jackie is the one who is moving.
5. The green light and red light travel at the same speed.
Which of these statements do both you and Jackie agree are true?