Deck 26: The Special Theory of Relativity

Question 1

Choose the one alternative that best completes the statement or answers the question.
The relativistic kinetic energy formula is valid

A) only for speeds near the speed of light.
B) only for subatomic particles, such as electrons and protons.
C) at all speeds.

Answer 1

C

Question 2

Choose the one alternative that best completes the statement or answers the question.
Suppose one twin takes a ride in a spaceship traveling at a very high speed to a distant star and then back again, while the other twin remains on Earth. Compared to the twin who remained on Earth, the astronaut twin is

A) older than the Earth-twin.
B) younger than the Earth-twin.
C) the same age as the Earth-twin.
D) The ages cannot be determined from the information provided.

Answer 2

B

Question 3

Choose the one alternative that best completes the statement or answers the question.
According to the equation $$E = m c ^ { 2 }$$ an object turns into energy when it reaches the speed of light.

Answer 3

False

Question 4

Choose the one alternative that best completes the statement or answers the question.
One of Einstein's postulates in formulating the special theory of relativity was that the laws of physics are the same in reference frames that

A) are stationary, but not in moving frames.
B) move at constant velocity with respect to an inertial frame.
C) accelerate.
D) oscillate.

Question 5

Choose the one alternative that best completes the statement or answers the question.
Which of the following are basic postulates of special relativity? (There could be more than one correct choice.)

A) No material object can be accelerated to the speed of light.
B) The laws of physics are the same in all reference frames.
C) The laws of physics are the same in all inertial reference frames.
D) The speed of light is the same for all observers.
E) Nothing can travel faster than the speed of light.

Question 6

Choose the one alternative that best completes the statement or answers the question.
If you were in a spaceship traveling close to the speed of light with respect to Earth, you would notice that

A) your mass was less than normal.
B) your pulse rate was greater than normal.
C) your mass was greater than normal.
D) some of your physical dimensions were smaller than normal.
E) none of the above effects occur.

Question 7

Choose the one alternative that best completes the statement or answers the question.
A really high-speed train moves in a direction parallel to its length with a speed that approaches the speed of light. The length of the train, as measured by a stationary observer on the ground,

A) is not affected by the motion.
B) increases due to the motion.
C) decreases due to the motion.
D) approaches infinity.

Question 8

Choose the one alternative that best completes the statement or answers the question.
A spaceship traveling at constant velocity passes by Earth and later passes by Mars. In which frame of reference is the amount of time separating these two events the proper time?

A) any frame of reference, inertial or not
B) the spaceship frame of reference
C) the Mars frame of reference
D) any inertial frame of reference
E) the Earth frame of reference

Question 9

Choose the one alternative that best completes the statement or answers the question.
Observer A sees a pendulum oscillating back and forth in a relativistic rocket and measures its period to be TA. Observer B moves along with the rocket and measures the period of the
Pendulum to be TB. What is true about these two time measurements? A) $T _ { A } = T _ { B }$
B) $T _ { A } > T _ { B }$
C) $T \mathrm {~A} < \mathrm { T } _ { \mathrm { B } }$
D) $T$ A could be greater or smaller than $T _ { B }$ depending on the direction of the motion.

Question 10

Choose the one alternative that best completes the statement or answers the question.
When an object moves close to the speed of light relative to Earth, what happens to its dimensions compared to what they were before it began moving, as measured by an Earth-based observer?

A) Only lengths perpendicular to the direction of travel are decreased.
B) Only lengths parallel to the direction of travel are decreased.
C) All lengths are decreased.
D) No lengths are affected.

Question 11

Choose the one alternative that best completes the statement or answers the question.
A spaceship is moving in a straight line away from Earth at 0.80c, measured relative to Earth. It launches a missile that moves away from the spaceship in the forward direction at 0.60c, relative to
The ship. Relative to Earth, what is the speed of this missile?

A) c
B) greater than 0.80c but less than c
C) greater than c but less than 1.4c
D) 1.4 c

Question 12

Choose the one alternative that best completes the statement or answers the question.
You are a passenger on a spaceship. As the speed of the spaceship increases, you will observe

A) no change in the length of your spaceship.
B) the length of your spaceship is zero.
C) the length of your spaceship getting shorter.
D) the length of your spaceship getting longer.

Question 13

Choose the one alternative that best completes the statement or answers the question.
You are a passenger on a spaceship. As the speed of the spaceship increases, you will observe

A) your watch gaining time.
B) nothing unusual about the behavior of your watch.
C) your watch slowing down.
D) your watch losing time.
E) your watch speeding up.

Question 14

Choose the one alternative that best completes the statement or answers the question.
Observer A sees a ruler moving by in a relativistic rocket and measures its length to be LA. Observer B moves along with the rocket and measures the length of the ruler to be LB. What is true
About these two length measurements? A) $L A < L _ { B }$
B) $L _ { A } > L _ { B }$
C) $L _ { A } = L _ { B }$
D) $L _ { A }$ could be greater or smaller than $L _ { B }$ depending on the direction of the motion.

Question 15

Choose the one alternative that best completes the statement or answers the question.
You are riding in a spaceship that has no windows, radios, or other means for you to observe or measure what is outside. You wish to determine if the ship is stopped or moving at constant
Velocity. How can you do this?

A) You can determine if the ship is moving by determining the apparent velocity of light in the spaceship.
B) You can determine if the ship is moving by lying down and measuring your height. If you are shorter than usual, the ship is moving.
C) You can determine if the ship is moving by checking your precision time piece. If it's running slow, the ship is moving.
D) You should give up because you have taken on an impossible task!

Question 16

Choose the one alternative that best completes the statement or answers the question.
A 30-year-old astronaut goes off on a long-term mission in a spacecraft that travels at speeds close to that of light. The mission lasts exactly 20 years as measured on Earth. Biologically speaking, at the end of the mission, the astronaut's age would be

A) exactly 30 years.
B) more than 50 years.
C) exactly 25 years.
D) less than 50 years.
E) exactly 50 years.

Question 17

Choose the one alternative that best completes the statement or answers the question.
The special theory of relativity predicts that there is an upper limit to the speed of an object. It therefore follows that there is also an upper limit on which of the following properties of the
Object? (There could be more than one correct choice.)

A) The linear momentum of the object.
B) The total energy of the object.
C) The kinetic energy of the object.
D) None of the above.

Question 18

Choose the one alternative that best completes the statement or answers the question.
A really high-speed train moves in a direction parallel to its length with a speed that approaches the speed of light. The height of the train, as measured by a stationary observer on the ground,

A) increases slightly.
B) decreases slightly.
C) approaches infinity.
D) approaches zero.
E) does not change due to the motion.

Question 19

Choose the one alternative that best completes the statement or answers the question.
You are moving at a speed 2/3 c toward Randy when shines a light toward you. At what speed do you see the light approaching you?

A) 1/3 c
B) c
C) 4/3 c
D) 2/3 c

Question 20

Choose the one alternative that best completes the statement or answers the question.
An astronaut is resting on a bed inclined at an angle above the floor of a spaceship, as shown in the figure. From the point of view of an observer who sees the spaceship moving near the speed of light parallel to the floor, the angle the bed makes with the floor

A) is the same as the angle observed by the astronaut.
B) is smaller than the angle observed by the astronaut.
C) is greater than the angle observed by the astronaut.
D) could be greater or smaller than the angle observed by the astronaut depending on whether the rocket is moving to the right or to the left.

Question 21

Write the word or phrase that best completes each statement or answers the question.
How fast (in terms of the speed of light) should a moving clock travel if it is to be observed
by a stationary observer as running at one-half its normal rate?

Question 22

Choose the one alternative that best completes the statement or answers the question.
A spaceship carrying a light clock moves at a speed of 0.960c relative to an observer on Earth. If the clock on the ship advances by 1.00 s as measured by the space travelers aboard the ship, how long
Did that advance take as measured by the observer on Earth? A) $5.8 \mathrm {~s}$
B) $2.6 \mathrm {~s}$
C) $0.96 \mathrm {~s}$
D) $1.2 \mathrm {~s}$
E) $3.6 \mathrm {~s}$

Question 23

Choose the one alternative that best completes the statement or answers the question.
A particle physicist observes cosmic rays creating a new particle high in the atmosphere, and the speed of this particle is measured at $99.7 \%$ the speed of light. It is unstable, and is observed to decay in an average $37.0 \mu \mathrm { s }$ . If this particle were at rest in the laboratory, what would be its average lifetime?

A) $4.3 \mu \mathrm { s }$
B) $12 \mu \mathrm { s }$
C) $5.3 \mu \mathrm { s }$
D) $2.9 \mu \mathrm { s }$
E) $18 \mu \mathrm { s }$

Question 24

Choose the one alternative that best completes the statement or answers the question.
An astronaut on a spaceship moving at 0.927c says that the trip between two stationary stars took 4.26 y. How long does this journey appear to take to someone in the rest frame of the two stars?

A) 1.60 y
B) 2.30 y
C) 12.6 y
D) 11.4 y

Question 25

Write the word or phrase that best completes each statement or answers the question.
A spaceship visits a star that is $4.5$ light-years from Earth, and the spaceship travels at one-half the speed of light for the entire trip.
(a) How long did the trip take according to an observer on Earth?
(b) How long did the trip take according to an observer on the spaceship?

Question 26

Write the word or phrase that best completes each statement or answers the question.
A muon at rest decays in $2.2 \mu$ s. Moving at $99.00 \%$ the speed of light, it would be seen to "live" for how long?

Question 27

Choose the one alternative that best completes the statement or answers the question.
Astronaut Rachel leaves Earth in a spaceship at a speed of $0.960 c$ relative to an observer on Earth. Rachel's destination is a star system $14.4$ light-years away (one light-year is the distance light travels in one year). According to Rachel, how long does the trip take?

A) 11 years
B) 23 years
C) $4.2$ years
D) 15 years
E) 14 years

Question 28

Choose the one alternative that best completes the statement or answers the question.
A spaceship approaches Earth with a speed $0.50$ c. A passenger in the spaceship measures his heartbeat as 70 beats per minute. What is his heartbeat rate according to an observer that is at rest relative to Earth?

A) 75 beats per minute
B) 69 beats per minute
C) 65 beats per minute
D) 73 beats per minute
E) 61 beats per minute

Question 29

Choose the one alternative that best completes the statement or answers the question.
A certain unstable particle has a mean lifetime of $1.52 \times 10 ^ { - 6 } \mathrm {~s}$ . This is the time interval between its creation in a nuclear process and its extinction into decay products, as measured in a frame of reference at rest with respect to the particle. An average such particle is observed by a scientist on Earth to travel $342 \mathrm {~m}$ in its lifetime. What is the speed of the particle relative to Earth? $( c = 3.00 \mathrm { x }$ $10 ^ { 8 } \mathrm {~m} / \mathrm { s }$ )

A) $0.821 c$
B) $0.551 \mathrm { c }$
C) $0.681 c$
D) $0.600 c$
E) $0.335 c$

Question 30

Choose the one alternative that best completes the statement or answers the question.
A pion is an unstable particle that has a mean lifetime of $2.55 \times 10 ^ { - 8 } \mathrm {~s}$ . This is the time interval between its creation in a nuclear process and its extinction into decay products, as measured in a frame of reference at rest with respect to the pion. An average pion is traveling at $0.230 \mathrm { c }$ relative to Earth. How far does it travel in its lifetime, relative to Earth?

A) $3.50 \mathrm {~m}$
B) $1.81 \mathrm {~m}$
C) $3.22 \mathrm {~m}$
D) $2.07 \mathrm {~m}$
E) $2.23 \mathrm {~m}$

Question 31

Choose the one alternative that best completes the statement or answers the question.
Someone in Earth's rest frame says that a spaceship's trip between two planets took $10.0 \mathrm { y }$ , while an astronaut on the space ship says that the trip took $5.78 \mathrm { y }$ . What is the speed of the spaceship, assuming the planets are at essentially at rest?

A) $0.816 \mathrm { c }$
B) $0.384 \mathrm { c }$
C) $0.735 \mathrm { c }$
D) $0.975 \mathrm { c }$

Question 32

Choose the one alternative that best completes the statement or answers the question.
A spaceship enters the solar system moving toward the sun at a constant speed relative to the sun. By its own clock, the time elapsed between the time it crosses the orbit of Jupiter and the time it crosses the orbit of Mars is $50.0$ minutes. As measured in the coordinate system of the sun, how Iong did it take for the spaceship to travel that distance? The radius of the orbit of Jupiter is $778 \times$ $10 ^ { 9 } \mathrm {~m}$ , and that of the orbit of Mars is $228 \times 10 ^ { 9 } \mathrm {~m}$ .

A) $58.6$ minutes
B) $30.0$ minutes
C) $95.8$ minutes
D) $69.8$ minutes
E) $43.6$ minutes

Question 33

Choose the one alternative that best completes the statement or answers the question.
At age 21, you set out for a star that is 50 light-years from Earth. How fast would your spaceship have to travel in order to reach that star when you are 61 years old? One light-year is the distance light travels in one year.

A) $0.96 c$
B) $0.88 c$
C) $0.58 \mathrm { c }$
D) $0.78 \mathrm { c }$
E) $0.68 c$

Question 34

Write the word or phrase that best completes each statement or answers the question.
An unstable particle is moving at a speed of $1.6 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s }$ relative to a laboratory. Its lifetime is measured by a stationary observer in the laboratory to be $6.8 \times 10 ^ { - 6 } \mathrm {~s}$ . What is the lifetime of the particle as measured in the rest frame of the particle? $\left( c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right)$

Question 35

Write the word or phrase that best completes each statement or answers the question.
You are moving past the Earth at 0.990c and notice your heart beating 88 beats per minute.
(a) If a doctor on Earth measures your heart rate as you zip past, what will the measured
rate be?
(b) If you had been moving 99.99% the speed of light, what rate would you have observed
your heart beats?

Question 36

Choose the one alternative that best completes the statement or answers the question.
A spaceship enters the solar system moving toward the Sun at a constant speed relative to the Sun. By its own clock, the time elapsed between the time it crosses the orbit of Jupiter and the time it crosses the orbit of Mars is $50.0$ minutes. How fast is the spaceship traveling towards the Sun? The radius of the orbit of Jupiter is $778 \times 10 ^ { 9 } \mathrm {~m}$ , and that of the orbit of Mars is $228 \times 10 ^ { 9 } \mathrm {~m}$ .

A) $0.522 c$
B) $0.982 c$
C) $0.438 c$
D) $0.319 c$
E) $0.671 c$

Question 37

Choose the one alternative that best completes the statement or answers the question.
A spaceship with a constant speed of 0.800c relative to Earth travels to a star that is 4.30 light-years from Earth. How much time for this trip would elapse on a clock on Earth?

A) 3.23 y
B) 5.38 y
C) 4.40 y
D) 5.15 y

Question 38

Choose the one alternative that best completes the statement or answers the question.
As measured in Earth's rest frame, a spaceship traveling at 0.9640c takes 10.5 y to travel between two planets that are not moving relative to each other. How long does the trip take as measured by
Someone on the spaceship?

A) 6.83 y
B) 2.79 y
C) 28.8 y
D) 39.5 y

Question 39

Choose the one alternative that best completes the statement or answers the question.
A spaceship with a constant speed of 0.800c relative to Earth travels to a star that is 4.30 light-years from Earth. How much time for this trip would elapse on a clock on board the spaceship?

A) 5.38 y
B) 3.23 y
C) 5.15 y
D) 4.40 y

Question 40

Choose the one alternative that best completes the statement or answers the question.
Astronaut Rob leaves Earth in a spaceship at a speed of $0.960 \mathrm { c }$ relative to an observer on Earth. Rob's destination is a star system $14.4$ light-years away (one light-year is the distance light travels in one year). Relative to a frame of reference that is fixed with respect to Earth, how long does it take Rob to complete the trip?

A) $4.20$ years
B) $14.4$ years
C) $10.8$ years
D) $22.7$ years
E) $15.0$ years

Question 41

Choose the one alternative that best completes the statement or answers the question.
Astronaut Hans leaves Earth in a spaceship traveling at a speed of 0.280c relative to the observer Brian at rest on Earth. Hans is holding a pencil at an angle of 30° with the direction of travel, as
Seen by Hans. What angle does the pencil make with the direction of travel, as seen by Brian on
Earth? A) $29 ^ { \circ }$
B) $33 ^ { \circ }$
C) $90 ^ { \circ }$
D) $30 ^ { \circ }$
E) $31 ^ { \circ }$

Question 42

Choose the one alternative that best completes the statement or answers the question.
A particle in a 799=m-long linear particle accelerator is moving at 0.875c. How long does the particle accelerator appear to the particle?

A) 387 m
B) 184 m
C) 1039 m
D) 1651 m

Question 43

Write the word or phrase that best completes each statement or answers the question.
A rocket is traveling away from Earth at 90% the speed of light. The captain turns on a
laser light. What is the speed of the light as measured by an Earth-based astronomer if the
captain aims the laser (a) directly forward or (b) directly backward?

Question 44

Write the word or phrase that best completes each statement or answers the question.
A person in a rocket ship traveling past the earth at a speed of 0.500c fires a laser gun in
the forward direction. With what speed does an observer on Earth measure for the light
pulse?

Question 45

Choose the one alternative that best completes the statement or answers the question.
Astronaut Sarah leaves Earth in a spaceship at a speed of 0.280c relative to Earth. Sarah's destination is a star system 12.5 light-years away (one light-year is the distance light travels in one
Year). According to Sarah, how far did she travel during the trip?

A) 12.5 light-years
B) 11.0 light-years
C) 11.5 light-years
D) 13.0 light-years
E) 12.0 light-years

Question 46

Write the word or phrase that best completes each statement or answers the question.
Two spaceships are approaching one another, each at a speed of 0.31c relative to a
stationary observer on Earth. What speed, in terms of the speed of light, does an observer
on one spaceship record for the other approaching spaceship?

Question 47

Choose the one alternative that best completes the statement or answers the question.
One 20-year-old twin brother takes a space trip with a speed of 0.80c for 30 years according to a clock on his spaceship. At the end of this trip, what are (a) his own age and (b) the age of his
Earth-based twin brother?

A) (a) 50 y (b) 70 y
B) (a) 20 y (b) 30 y
C) (a) 70 y (b) 90 y
D) (a) 30 y (b) 50 y

Question 48

Choose the one alternative that best completes the statement or answers the question.
A spaceship with a constant velocity of 0.800c relative to Earth travels to the star that is 4.30 light-years from Earth. What distance does the space ship travel as measured by a passenger on
The ship? A) $4.30$ light-years
B) $2.58$ light-years
C) $3.52$ light-years
D) $4.12$ light-years

Question 49

Choose the one alternative that best completes the statement or answers the question.
The figure shows a right-angled construction frame $\mathrm { ABC }$ . When measured at rest, it has dimensions as follows: $\mathrm { AB } = 26.0 \mathrm {~m} , \mathrm { AC } = 10.0 \mathrm {~m}$ , and $\mathrm { BC } = 24.0 \mathrm {~m}$ . This frame is now given a new velocity of $0.760$ c, relative to Earth, in a direction parallel to AC. How long is part AC of this frame with the new velocity as measured by Earth-based engineers?

A) $24.9 \mathrm {~m}$
B) $6.50 \mathrm {~m}$
C) $25.4 \mathrm {~m}$
D) $23.7 \mathrm {~m}$
E) $24.3 \mathrm {~m}$

Question 50

Choose the one alternative that best completes the statement or answers the question.
How fast must a meter stick move, relative to the frame of the observer making the measurement, so its length will be measured to be 0.60 m?

A) 0.40c
B) 0.60c
C) 0.90c
D) 0.80c
E) 0.70c

Question 51

Choose the one alternative that best completes the statement or answers the question.
Astronaut Jill leaves Earth in a spaceship and is now traveling at a speed of 0.280c relative to an observer on Earth. When Jill left Earth, the spaceship was equipped with all kinds of scientific
Instruments, including a meter stick. Now that Jill is underway, how long does she measure the
Meter stick to be?

A) 1.04 m
B) 1.28 m
C) 1.00 m
D) 0.960 m
E) 0.280 m

Question 52

Write the word or phrase that best completes each statement or answers the question.
A spacecraft is measured by a scientist on the ground to have a length of $81 \mathrm {~m}$ as it flies overhead with a speed $2.4 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s }$ . The spacecraft then lands and its length is again measured by the scientist at rest on the ground. What result does he now get for the Iength of the spacecraft? $\left( c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right)$

Question 53

Choose the one alternative that best completes the statement or answers the question.
The figure shows a right-angled construction frame $A B C$ . When measured at rest, it has dimensions as follows: $A B = 18.9 \mathrm {~m} , A C = 10.0 \mathrm {~m}$ , and $B C = 16.0 \mathrm {~m}$ . This frame is now given a new velocity of $0.420$ c, relative to Earth, in a direction parallel to $A C$ . How long is part $B C$ of this frame with the new velocity as measured by Earth-based engineers?

A) $16.0 \mathrm {~m}$
B) $10.0 \mathrm {~m}$
C) $12.0 \mathrm {~m}$
D) $18.0 \mathrm {~m}$
E) $14.0 \mathrm {~m}$

Question 54

Choose the one alternative that best completes the statement or answers the question.
Two stars are at rest relative to each other. A spaceship is moving between these two stars at 0.932c relative to each star. To someone in the ship, the distance between the two stars appears to be
26)4 light-years. What is the distance between the stars in their own rest frame?

A) 72.8 light-years
B) 55.4 light-years
C) 9.57 light-years
D) 21.1 light-years

Question 55

Write the word or phrase that best completes each statement or answers the question.
A stretch of land is 12.5 km long on a map.
(a) What would be its length to an observer moving by, parallel to the stretch, at 0.9500c?
(b) Which is the proper length for this stretch of land?
(c) How fast relative to Earth would the observer have to move for the land to appear 6.50
km long? Express your answer in terms of the speed of light.

Question 56

Write the word or phrase that best completes each statement or answers the question.
How fast would a rocket ship have to move past Earth to contract to half of its proper
length as observed by an Earth-based physicist?

Question 57

Write the word or phrase that best completes each statement or answers the question.
A starship is constructed to be 100 m long in the factory. It is launched and as it coasts by
Earth, it is measured to be shortened to 5.48 m long.
(a) How fast, in terms of the speed of light, is it moving past Earth?
(b) What length does the ship's crew measure for the ship?

Question 58

Choose the one alternative that best completes the statement or answers the question.
A set of twins, Andrea and Courtney, are initially 10 years old. While Courtney remains on Earth, Andrea rides on a spaceship that travels away from Earth at a speed of 0.60c for 10 years (as
Measured by Courtney). At the end of the trip, Courtney is 20 years old. How old is Andrea?

A) 12 years
B) 10 years
C) 20 years
D) 18 years

Question 59

Write the word or phrase that best completes each statement or answers the question.
From the Earth, the Earthlings see the Enterprise approaching from the west at 0.800c and
the Klingons approaching from the east at 0.900c. What speed, in terms of the speed of
light, does the crew of the Enterprise measure for the Klingon ship?

Question 60

Choose the one alternative that best completes the statement or answers the question.
Two stars are at rest relative to each other. In their common rest frame, these stars are 90.0 light-years apart. If they are measured to be 68.7 light-years apart by the navigator of a spaceship
Traveling between them, how fast is the spaceship moving relative to these stars?

A) 0.558c
B) 0.604c
C) 0.505c
D) 0.646c

Question 61

Write the word or phrase that best completes each statement or answers the question.
Two spaceships are traveling through space at speeds of 0.600c and 0.900c, respectively,
with respect to Earth. If they are headed directly toward each other, what is their
approach speed (in terms of the speed of light) as measured by the captain of either ship?

Question 62

Choose the one alternative that best completes the statement or answers the question.
A spaceship, traveling at 0.560c towards a stationary space platform, launches a secondary towards the station with a speed of 0.100c relative to the spaceship. What is the speed of the
Secondary rocket relative to the space platform?

A) 0.600c
B) 0.575c
C) 0.625c
D) 0.660c
E) 0.460c

Question 63

Choose the one alternative that best completes the statement or answers the question.
A spaceship, traveling at 0.100c away from a stationary space platform, launches a secondary rocket towards the station, with a speed of 0.560c relative to the spaceship. What is the speed of the
Secondary rocket relative to the space platform?

A) 0.550c
B) 0.492c
C) 0.487c
D) 0.660c
E) 0.460c

Question 64

Choose the one alternative that best completes the statement or answers the question.
Consider three galaxies, Alpha, Beta and Gamma. An astronomer in Beta sees each of the other two galaxies moving away from her in opposite directions at $0.70 \mathrm { c }$ . At what speed would an observer in Alpha see the galaxy Beta moving?

A) $0.70 c$
B) $0.82 c$
C) $0.94 c$
D) $0.35 c$
E) $0.57 c$

Question 65

Choose the one alternative that best completes the statement or answers the question.
Two spaceships approach Earth from opposite directions. One has a speed of 0.21c and the other a speed of 0.34c, both relative to Earth. What is the speed of one spaceship relative to the other?

A) 0.58c
B) 0.55c
C) 0.64c
D) 0.61c
E) 0.51c

Question 66

Write the word or phrase that best completes each statement or answers the question.
Two spaceships approach each other along a straight line at a constant relative velocity of
0.9880c as measured by the captain of one of the ships. An observer on Earth is able to
measure the speed of only one of the ships as 0.9000c. From the point of view of the
observer on Earth, what is the speed of the other ship in terms of the speed of light?

Question 67

Choose the one alternative that best completes the statement or answers the question.
Two spaceships, each 100 m long in its own rest frame, approach Earth from opposite directions, with equal speeds relative to Earth. As measured by a passenger in one of the spaceships, the other
Spaceship is 96 m long. What is the speed of the spaceships relative to Earth?

A) c/4
B) c/6
C) c/3
D) c/5
E) c/7

Question 68

Choose the one alternative that best completes the statement or answers the question.
Two spaceships approach Earth from the same direction. One has a speed of 0.21c and the other a speed of 0.34c, both relative to Earth. What is the speed of one spaceship relative to the other?

A) 0.18c
B) 0.16c
C) 0.14c
D) 0.13c
E) 0.15c

Question 69

Choose the one alternative that best completes the statement or answers the question.
As shown in the figure, the captain of spaceship A observes spaceship $E$ escaping with a relative velocity of $0.35 c$ . A missile $M$ is fired from ship A directly toward ship $E$ , with a velocity of $0.76 c$ relative to ship A. What does the captain of ship E measure for the velocity of the missile M?

A) $0.41 \mathrm { c }$
B) $0.45 c$
C) $0.56 c$
D) $0.52 c$
E) $0.48 c$

Question 70

Choose the one alternative that best completes the statement or answers the question.
Two spaceships, each 100 m long in its own rest frame, approach Earth from opposite directions, each with a speed 0.50c relative to Earth. As measured by a passenger in one of the spaceships,
How long is the other spaceship?

A) 70 m
B) 60 m
C) 80 m
D) 50 m
E) 90 m

Question 71

Choose the one alternative that best completes the statement or answers the question.
A spaceship is moving away from an asteroid with a speed of 0.80c relative to the asteroid. The spaceship then fires a missile with a speed of 0.50c relative to the spaceship. What is the speed of
The missile measured by astronauts on the asteroid if the missile is fired toward the asteroid?

A) 0.30c
B) 1.3c
C) 0.50c
D) 0.65c
E) 0.93c

Question 72

Choose the one alternative that best completes the statement or answers the question.
A star is moving toward Earth at 90% the speed of light. The star emits light, which moves away from the star at the speed of light. What do Earth-based astronomers measure for the speed of this
Light?

A) 1.2c
B) 0.98c
C) c
D) 0.95c
E) 1.9c

Question 73

Choose the one alternative that best completes the statement or answers the question.
A spaceship is moving away from an asteroid with a speed of 0.80c relative to the asteroid. The spaceship then fires a missile with a speed of 0.50c relative to the spaceship. What is the speed of
The missile measured by astronauts on the asteroid if the missile is fired away from the asteroid?

A) 0.50c
B) 0.65c
C) 0.93c
D) 0.30c
E) 1.3c

Question 74

Choose the one alternative that best completes the statement or answers the question.
In an "atom smasher," two particles collide head on at relativistic speeds. If the velocity of the first particle is 0.741c to the left, and the velocity of the second particle is 0.543c to the right (both as
Measured in the lab rest frame), how fast are the particles moving with respect to each other?

A) 0.834c
B) 0.934c
C) 0.916c
D) 1.284c

Question 75

Choose the one alternative that best completes the statement or answers the question.
A spaceship leaves Earth at a steady forward speed of 70% the speed of light. How fast relative to the ship must the spaceship launch a shuttlecraft in the forward direction so that it will be moving
Away from Earth at 98.7% the speed of light?

A) 0.84c
B) 0.97c
C) 0.91c
D) 0.99c
E) 0.93c

Question 76

Choose the one alternative that best completes the statement or answers the question.
A spaceship approaching an asteroid at a speed of 0.60c launches a scout rocket with speed 0.40c relative to the spaceship. At what speed is the scout rocket approaching the asteroid?

A) 1.0c
B) 0.64c
C) 0.96c
D) 0.76c
E) 0.81c

Question 77

Choose the one alternative that best completes the statement or answers the question.
A spaceship traveling at 0.50c away from Earth launches a secondary rocket in the forward direction at 0.50c relative to the spaceship. As measured by Earthlings, how fast is the secondary
Rocket moving away from Earth?

A) c
B) 0.70c
C) 0.50c
D) 0.80c
E) 0.90c

Question 78

Choose the one alternative that best completes the statement or answers the question.
Three spaceships A, B, and C are in motion as shown in the figure. The commander on ship B observes ship C approaching with a relative velocity of $0.82 c$ . The commander also observes ship A, advancing in the rear, with a relative velocity of $0.50 \mathrm { c }$ . What is the speed of ship $\mathrm { C }$ as measured by the captain of ship A?

A) $22 c$
B) $0.54$
C) $1.3 c$
D) $0.94 c$
E) $0.23 c$

Question 79

Choose the one alternative that best completes the statement or answers the question.
Consider three galaxies, Alpha, Beta and Gamma. An astronomer in Beta sees each of the other two galaxies moving away from him in opposite directions at 0.70c. At what speed would an
Observer in Alpha see the galaxy Gamma moving?

A) 0.94c
B) 0.98c
C) 0.82c
D) 0.70c
E) 1.4c

Question 80

Write the word or phrase that best completes each statement or answers the question.
A tracking station on Earth observes a rocket move away at 0.370c. This rocket is designed
to launch a projectile at 0.505c relative to the rocket. What speed (in terms of the speed of
light) does the tracking station measure for the projectile if it is fired (a) straight ahead of
the rocket or (b) backward from the rocket?