See attached file for full problem description.

When Time Flies...It Runs More Slowly

Learning Goal: To understand length contraction and time dilation.

In classical physics, and in your everyday experience, lengths and times

seem to be the same no matter who measures them. In fact, the notion

that lengths or time intervals might be different depending on who

measures them can seem profoundly disturbing (or just plain silly),

because measuring space and time are two of the most fundamental ideas

in physics. However, Einstein's special theory of relativity shows that

space and time are not as fundamental or as absolute as you are

accustomed to believing.

To discuss measurements more precisely, you must consider both the thing

being measured and the person (technically the frame of reference) doing

the measuring. An inertial frame of reference is a frame of reference

(i.e., a consistent way of measuring distances and times) that is not

accelerating. An inertial frame of reference moves at a constant speed,

relative to other inertial frames of reference.

between the two frames. The measured length and time are given by the

following two equations:

,

is the measured length in the direction of motion.

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Part A

?

in meters to three significant figures.

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Part B

passes on the clock?

Express your answer in seconds to three significiant figures.

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.

Part C

will the captain of ship B measure to have passed between the firing of

the two missiles?

Express your answer in seconds to three significant figures.

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Part D

of the missile, relative to ship B?

.

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). Your calculator may not be able to store enough digits to work these

problems accurately, so you may need to use the approximations from the

binomial expansion:

Part E

)? The answer is small but nonzero. You will need to find an expression

for the time difference using the approximation given in this problem

before you substitute in the numbers; otherwise your calculator will

just give zero.

.

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Part F

(a reasonable proper length for a car)? Use a similar procedure to the

one you used in the previous part.

.

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