As measured by an observer on the earth, a spacecraft runway on earth has a leng

Question

As measured by an observer on the earth, a spacecraft runway on earth has a length of 3900 m .

Part A

What is the length of the runway as measured by a pilot of a spacecraft flying past at a speed of 3.70×107m/s relative to the earth?

Express your answer using three significant figures.

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Part B

An observer on earth measures the time interval from when the spacecraft is directly over one end of the runway until it is directly over the other end. What result does she get?

Express your answer using three significant figures.

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Part C

The pilot of the spacecraft measures the time it takes him to travel from one end of the runway to the other end. What value does he get?

Express your answer using three significant figures.

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As measured by an observer on the earth, a spacecraft runway on earth has a length of 3900 m .

Part A

What is the length of the runway as measured by a pilot of a spacecraft flying past at a speed of 3.70×107m/s relative to the earth?

Express your answer using three significant figures.

L=   m

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Part B

An observer on earth measures the time interval from when the spacecraft is directly over one end of the runway until it is directly over the other end. What result does she get?

Express your answer using three significant figures.

t=   s

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Part C

The pilot of the spacecraft measures the time it takes him to travel from one end of the runway to the other end. What value does he get?

Express your answer using three significant figures.

t0=   s

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Explanation / Answer

L = 3.9 km

L' = L/

= 1 / 1 - v²/c² = 1 / 1 - 13.69x10^14/9x10^16

= 1/0.992 = 1.008

L' = L/1.008 = 3869 m

b)
t = L/v
t = 3900 m/3.7x10^7 = 0.10540*10^-3 s

c)

t' = t/ = 0.105*10^-3 /1.008 = L'/v = 3869/3.7x10^7 = 0.10529*10^-3 s

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