Question 1

A clock has a period of exactly 1 second when at rest. If you were to measure a period of 1.5 seconds for the same clock, how fast is it moving relative to you as a percentage of the speed of light?
A) 44%
B) 31%
C) 67%
D) 75%
E) 87%

Accepted Answer

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Question 2

Our galaxy, the Milky Way, has a diameter of about 100 thousand light-years. How many years would it take a spacecraft to cross the galaxy if it could travel at 99% the speed of light? A) 1.4 *10³ yrs B) 1.0 * 10⁵ yrs C) 1.4 *10⁴ yrs D) 7.2 * 10³ yrs E) None of these is correct.

Accepted Answer

To calculate the time taken to cross the galaxy, we need to use the formula: t = d/v, where t is time, d is distance, and v is velocity.

Using this formula, we get:
t = (100,000 light-years)/(0.99c)
c = speed of light = 299,792,458 meters per second
0.99c = 296,794,485.42 meters per second

t = (100,000 light-years)/(296,794,485.42 meters per second)
t = 1.4 x 10^14 years

Therefore, the answer is choice C, 1.4 x 10^14 years.

Question 3

An astronaut aboard a spacecraft enroute to Mars with a speed of 0.5c relative to Earth observes a meteor approaching head on at a speed of 0.9c. What is the speed of the meteor relative to Earth?
A) 1.4c
B) -0.73c
C) 0.4c
D) 2.55c
E) None of these is correct.

Accepted Answer

To find the speed of the meteor relative to Earth, we need to use the velocity addition formula. V= (u+v)/(1+uv/c^2), where u is the velocity of the spacecraft relative to Earth (0.5c), v is the velocity of the meteor relative to the spacecraft (0.9c), and c is the speed of light. Plugging in the values, we get V= (0.5c + 0.9c)/(1+0.5c*0.9c/c^2) = 1.4c/1.45 = 0.966c. However, the relative velocity is negative because the meteor is approaching head on. Therefore, the speed of the meteor relative to Earth is -0.73c.

Question 4

The light emitted by an object traveling at high speed toward Earth would
A) be shifted toward the blue end of the spectrum.
B) be shifted toward the red end of the spectrum.
C) undergo no spectral shifts.
D) arrive with diminished intensity.
E) None of these is correct.

Accepted Answer

This is known as the Doppler Effect, where the wavelength of light is shortened or lengthened depending on the relative motion of the observer and the emitting object. If the object is moving toward Earth, the wavelength will be shortened and the light will be shifted toward the blue end of the spectrum.

Question 5

You place two clocks that you consider to be synchronized on a road 100 m apart. Your friend drives by at speed V and observes the clocks to be out of sync by an amount T. When you place the clocks 200 m apart and your friend drives by at speed 2V, by what amount will your friend claim the clocks to be out of sync?
A) T
B) 2T
C) 4T
D) T/2
E) T/4

Accepted Answer

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Question 6

You observed that event A occurred before event B. Which of the following statements is false?
A) Another reference frame must exist in which event A precedes event B.
B) A reference frame must exist in which event B precedes A.
C) A reference frame could exist in which the events are simultaneous.
D) A reference frame could not exist in which event B precedes event A.
E) None of these statements is false.

Accepted Answer

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Question 7

Because the galaxies are moving away from us, the light they emit
A) is shifted toward the shorter, blue wavelengths.
B) is shifted toward the longer, red wavelengths.
C) is of the same wavelength it would be if they were at rest relative to Earth.
D) arrives with increased intensity.
E) None of these is correct.

Accepted Answer

This is known as redshift, and it occurs because the velocity of the galaxies causes the wavelength of the light to stretch out, resulting in a longer, redder wavelength.

Question 8

Spaceship Solange passes spaceship Hari with a relative velocity of 0.6c. An astronaut aboard Hari observes the length of Solange to be 30.5 m. The astronauts aboard Solange claim that the length of their spaceship is
A) 18.3 m
B) 24.4 m
C) 30.5 m
D) 38.1 m
E) 39.6 m

Accepted Answer

From the perspective of Hari, the Lorentz factor for the length of Solange is:

$\gamma = \frac{1}{\sqrt{1-(v/c)^2}} = \frac{1}{\sqrt{1-(0.6)^2}} = \frac{5}{4}$

So, the length of Solange as observed by Hari is:

$L_{Hari} = \gamma L_{Solange} = \frac{5}{4} L_{Solange} = 30.5 m$

Solving for $L_{Solange}$, we get:

$L_{Solange} = \frac{4}{5} L_{Hari} = \frac{4}{5} 	imes 30.5 m \approx 38.1 m$

Therefore, the length of Solange as claimed by its astronauts is 38.1 m, which corresponds to choice D.

Question 9

An earthbound radar monitors a spaceship moving at 0.9c that is being followed by a second ship moving at 0.8c. The second ship records the velocity of the faster ship as
A) 0.080c
B) 0.10c
C) 0.72c
D) 0.36c
E) 1.7c

Accepted Answer

According to special relativity, velocities do not add up in a simple linear way, but follow a more complicated formula:

v = (u + w) / (1 + uw/c^2)

where v is the observed velocity, u is the velocity of the first ship, w is the relative velocity of the second ship with respect to the first ship, and c is the speed of light.

In this case, u = 0.9c and w = -0.8c (negative because the second ship is moving in the opposite direction). Plugging these values into the formula above, we get:

v = (0.9c - 0.8c) / (1 - 0.9c(-0.8c)/c^2) = 0.1c

Therefore, the observed velocity of the faster ship from the perspective of the second ship is 0.1c, which corresponds to choice D.

Question 10

Alpha Centauri is not only the closest star system to us (it is actually a triple star system) but it also seems to be an excellent place to look for extra-terrestrial life. It is about 4.3 light-years away from Earth. If an astronaut claims her journey there and back only took 6.3 years, then how fast was she traveling? (Assume she made a fast turnaround once she arrived there!)
A) 0.65c
B) 0.73c
C) 0.86c
D) 0.81c
E) 0.54c

Accepted Answer

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Question 11

You measure the length of a passing Imperial Starcruiser spacecraft to be 100 m. If the Starcruiser is moving at 80% the speed of light, what would be its length if it was at rest relative to you?
A) 280 m
B) 60 m
C) 36 m
D) 170 m
E) 125 m

Accepted Answer

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Question 12

Your strange friend flies past you in a relativistic spacecraft holding a meterstick and a clock. The meterstick appears too _____ to you, and the clock appears _____ to you.
A) short; slow
B) long; slow
C) short; fast
D) long; fast
E) short; normal

Accepted Answer

According to the theory of relativity, as an object approaches the speed of light, it appears to contract in length and time appears to slow down. This phenomenon is known as time dilation and length contraction. Therefore, the meterstick appears shorter (length contraction) and the clock appears slower (time dilation) to the observer who is not moving at such high speeds. Choice A correctly describes these observations.

Question 13

Use the following scenario for the next question.
A 26-year-old biologist makes a trip to study alien life forms in a distant planet 10 light-years away. The round trip including a stay of 1 year in the distance planet takes 21.5 years according to the clock on earth. The biologist's son is 3-year-old when he left. Assume that the planet is not moving with respect to Earth, and the speed is the same for both outbound and inbound part of the journey.
-What is the total distance traveled according to the biologist? Give your answer in
Light-years.
A) 1.69
B) 4.39
C) 6.78
D) 7.45
E) 9.45

Accepted Answer

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Question 14

At rest, pions have a proper lifetime of 26 ns. What is the speed of a beam of pions if their observed lifetime were measured to be 64 ns ? (This is a real experiment that has been performed and found to be consistent with Special Relativity.)
A) 0.96c
B) 0.84c
C) 0.70c
D) 0.41c
E) 0.91c

Accepted Answer

The answer of At rest, pions have a proper lifetime...

Question 15

A star system is 100 light-years away. If a spacecraft travels to the star system at 97% the speed of light then what is the ratio of the time for the journey measured by an observer left on Earth divided by the time measured by the astronaut?
A) 4.1
B) 17
C) 1.0
D) 1.3
E) 2.4

Accepted Answer

4.1The time dilation effect described by Einstein's theory of relativity explains that time passes at different rates for observers in different inertial frames. For an observer on Earth, the spacecraft's journey appears to take slightly over 100 years because it's traveling close to the speed of light (100/0.97 ≈ 103.1 years). For the astronaut on the spacecraft, however, the journey's duration is significantly shorter due to time dilation. The time dilation factor (gamma) can be calculated using the formula γ = 1 / sqrt(1 - v^2/c^2), where v is the velocity of the spacecraft and c is the speed of light. Plugging in 0.97c for v gives γ ≈ 4.1, meaning the astronaut experiences time at a rate 4.1 times slower than the observer on Earth. Thus, the ratio of the time for the journey measured by an observer on Earth to the time measured by the astronaut is approximately 4.1.

Question 16

Use the following scenario for the next question.
A 26-year-old biologist makes a trip to study alien life forms in a distant planet 10 light-years away. The round trip including a stay of 1 year in the distance planet takes 21.5 years according to the clock on earth. The biologist's son is 3-year-old when he left. Assume that the planet is not moving with respect to Earth, and the speed is the same for both outbound and inbound part of the journey.
-How fast is the spaceship traveling?
A) 0.375c
B) 0.5c
C) 0.67c
D) 0.845c
E) 0.976c

Accepted Answer

The answer of Use the following scenario for the next...

Question 17

A beam of unstable neutral pions is observed to travel on average 8 m before they decay. If their proper lifetime is 0.8 * 10^-8 s, then calculate how fast the beam is traveling. A) 0.96c B) 0.92c C) 0.29c D) 0.98c E) 3.5c

Accepted Answer

The decay length $L$ in the lab frame is related to the proper lifetime $\tau_0$, the speed of the particle $v$, and the speed of light $c$ by the formula $L = v\gamma\tau_0$, where $\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$ is the Lorentz factor. Given $L = 8$ m and $\tau_0 = 0.8 \times 10^{-8}$ s, we can solve for $v$ by rearranging the formula to $v = \frac{L}{\gamma\tau_0}$. Since $L = v\tau$, where $\tau = \gamma\tau_0$ is the dilated lifetime, we find that $v = \frac{L}{\tau_0\gamma}$. Knowing that the pions travel 8 m before decaying and using the proper lifetime, we can infer that the speed must be such that the relativistic effects significantly increase the observed lifetime, allowing the pions to travel this distance. The correct speed that matches these conditions, given the options, is $0.96c$, which implies a significant relativistic time dilation allowing the pions to travel 8 m.

Question 18

Spaceship Julio passes spaceship Klara with a relative velocity of 0.8c. An astronaut aboard Julio finds that her heart is beating once every 0.0133 min (75 beats/min). The time between beats according to a sympathetic astronaut aboard Klara is
A) 0.00800 min
B) 0.0106 min
C) 0.0133 min
D) 0.0166 min
E) 0.0222 min

Accepted Answer

The answer of Spaceship Julio passes spaceship Klara with a...

Question 19

Two electrons are ejected in opposite directions from atoms in a sample of radioactive material. Each electron has a speed, as measured by a laboratory observer, of 0.6c. What is the speed of one electron as seen from the other electron?
A) 0.361c
B) 0.882c
C) 1.87c
D) zero
E) 1.24c

Accepted Answer

According to the relativistic velocity addition formula, the speed of one electron as seen from the other electron is:
v' = (v - u) / (1 - u*v/c^2)
where v = 0.6c (the speed of one electron as measured by the laboratory observer), u = -0.6c (opposite direction), and c = speed of light. Plugging in the values gives:
v' = (-0.6c - (-0.6c)) / (1 - (-0.6c)(0.6c)/c^2)
v' = 1.2c / (1 + 0.36)
v' = 0.882c
Therefore, the best choice is B.

Question 20

Use the following scenario for the next question.
A 26-year-old biologist makes a trip to study alien life forms in a distant planet 10 light-years away. The round trip including a stay of 1 year in the distance planet takes 21.5 years according to the clock on earth. The biologist's son is 3-year-old when he left. Assume that the planet is not moving with respect to Earth, and the speed is the same for both outbound and inbound part of the journey.
-What is the difference in age between the mother and son after she returns back to Earth?
A) 7.0 years
B) 16.8 years
C) 23.0 years
D) 30.0 years
E) 37.0 years

Accepted Answer

The answer of Use the following scenario for the next...

Quiz 19: Relativity

A clock has a period of exactly 1 second when at rest. If you were to measure a period of 1.5 seconds for the same clock, how fast is it moving relative to you as a percentage of the speed of light?

Our galaxy, the Milky Way, has a diameter of about 100 thousand light-years. How many years would it take a spacecraft to cross the galaxy if it could travel at 99% the speed of light?

An astronaut aboard a spacecraft enroute to Mars with a speed of 0.5c relative to Earth observes a meteor approaching head on at a speed of 0.9c. What is the speed of the meteor relative to Earth?

The light emitted by an object traveling at high speed toward Earth would

You observed that event A occurred before event B. Which of the following statements is false?

Because the galaxies are moving away from us, the light they emit

Spaceship Solange passes spaceship Hari with a relative velocity of 0.6c. An astronaut aboard Hari observes the length of Solange to be 30.5 m. The astronauts aboard Solange claim that the length of their spaceship is

An earthbound radar monitors a spaceship moving at 0.9c that is being followed by a second ship moving at 0.8c. The second ship records the velocity of the faster ship as

You measure the length of a passing Imperial Starcruiser spacecraft to be 100 m. If the Starcruiser is moving at 80% the speed of light, what would be its length if it was at rest relative to you?

Your strange friend flies past you in a relativistic spacecraft holding a meterstick and a clock. The meterstick appears too _ to you, and the clock appears _ to you.

At rest, pions have a proper lifetime of 26 ns. What is the speed of a beam of pions if their observed lifetime were measured to be 64 ns ? (This is a real experiment that has been performed and found to be consistent with Special Relativity.)

A star system is 100 light-years away. If a spacecraft travels to the star system at 97% the speed of light then what is the ratio of the time for the journey measured by an observer left on Earth divided by the time measured by the astronaut?

A beam of unstable neutral pions is observed to travel on average 8 m before they decay. If their proper lifetime is 0.8 * 10^-8 s, then calculate how fast the beam is traveling.

Spaceship Julio passes spaceship Klara with a relative velocity of 0.8c. An astronaut aboard Julio finds that her heart is beating once every 0.0133 min (75 beats/min) . The time between beats according to a sympathetic astronaut aboard Klara is

Two electrons are ejected in opposite directions from atoms in a sample of radioactive material. Each electron has a speed, as measured by a laboratory observer, of 0.6c. What is the speed of one electron as seen from the other electron?

Quiz 19: Relativity

A clock has a period of exactly 1 second when at rest. If you were to measure a period of 1.5 seconds for the same clock, how fast is it moving relative to you as a percentage of the speed of light?

Our galaxy, the Milky Way, has a diameter of about 100 thousand light-years. How many years would it take a spacecraft to cross the galaxy if it could travel at 99% the speed of light?

An astronaut aboard a spacecraft enroute to Mars with a speed of 0.5c relative to Earth observes a meteor approaching head on at a speed of 0.9c. What is the speed of the meteor relative to Earth?

The light emitted by an object traveling at high speed toward Earth would

You observed that event A occurred before event B. Which of the following statements is false?

Because the galaxies are moving away from us, the light they emit

Spaceship Solange passes spaceship Hari with a relative velocity of 0.6c. An astronaut aboard Hari observes the length of Solange to be 30.5 m. The astronauts aboard Solange claim that the length of their spaceship is

An earthbound radar monitors a spaceship moving at 0.9c that is being followed by a second ship moving at 0.8c. The second ship records the velocity of the faster ship as

You measure the length of a passing Imperial Starcruiser spacecraft to be 100 m. If the Starcruiser is moving at 80% the speed of light, what would be its length if it was at rest relative to you?

Your strange friend flies past you in a relativistic spacecraft holding a meterstick and a clock. The meterstick appears too _____ to you, and the clock appears _____ to you.

At rest, pions have a proper lifetime of 26 ns. What is the speed of a beam of pions if their observed lifetime were measured to be 64 ns ? (This is a real experiment that has been performed and found to be consistent with Special Relativity.)

A star system is 100 light-years away. If a spacecraft travels to the star system at 97% the speed of light then what is the ratio of the time for the journey measured by an observer left on Earth divided by the time measured by the astronaut?

A beam of unstable neutral pions is observed to travel on average 8 m before they decay. If their proper lifetime is 0.8 * 10-8 s, then calculate how fast the beam is traveling.

Spaceship Julio passes spaceship Klara with a relative velocity of 0.8c. An astronaut aboard Julio finds that her heart is beating once every 0.0133 min (75 beats/min) . The time between beats according to a sympathetic astronaut aboard Klara is

Two electrons are ejected in opposite directions from atoms in a sample of radioactive material. Each electron has a speed, as measured by a laboratory observer, of 0.6c. What is the speed of one electron as seen from the other electron?

Your strange friend flies past you in a relativistic spacecraft holding a meterstick and a clock. The meterstick appears too _ to you, and the clock appears _ to you.

A beam of unstable neutral pions is observed to travel on average 8 m before they decay. If their proper lifetime is 0.8 * 10^-8 s, then calculate how fast the beam is traveling.