# Problem Set

```AP Physics C
Problem Set Unit 4 - Relativity
1. The principle of classical (Newtonian) relativity a) did not seem to apply to electricity and magnetism
b) required a constant speed of light different from that predicted by Maxwell’s equations c) implied that
nothing can travel faster than the speed of light d) all of the above e) none of the above.
2. The Michelson-Morley experiment showed that the speed of light in a vacuum a) depends on the
observer’s motion b) is constant for all observers regardless of their motion c) proved that the luminiferous
ether exists d) all of the above e) none of the above
3. Events that are simultaneous in one inertial reference frame are a) always simultaneous in other inertial
reference frames b) never simultaneous in other inertial reference frames c) sometimes simultaneous in
other inertial reference frames
4. In a space war, a warrior traveling at a speed of 0.85c heads directly toward a laser. At what speed does the
warrior see the light from the laser approach him? a) 0.15c b) 0.85c c) c d) 1.15c e) 1.85c
5. An observer, Shirley Ujest, sees a friend, Ima Niodiot, passing by her in a rocket ship traveling at a constant
velocity well above 0.5c. Shirley knows that Ima is 5 feet tall, and has very long arms that reach 6 feet across.
Ima is standing perpendicular to the motion of the ship with her hands extended sideways. Shirley sees a
a) less than 5 foot tall Ima with a wingspan of less than 6 feet. b) more than 5 foot tall Ima with a wingspan of
more than 6 feet. c) 5 foot tall Ima with a wingspan of 6 feet. d) Any of the above are possible.
e) None of the above.
6. A long, thin rocket takes off straight up from the ground. It is observed by three people: a man selling ice
cream on the beach, a woman riding upward in an adjacent gantry elevator, and the pilot looking out the
window. Referring to the rocket’s length a) the pilot sees the shortest length b) the woman sees the
shortest length c) the ice cream man sees the shortest length d) all of them see the same length
7. An astronaut heading out toward a star at a constant high velocity can determine he is in motion by
a) the contraction of on-board meter sticks b) the slowing down of time on his clocks c) the increase of his
mass d) all of these e) none of these
8. A spacecraft moves past a student, Al Titude, with a relative velocity of 0.90c. If the pilot of the spacecraft,
Hans Zoff, sees 10 minutes elapse on his watch, how much time has elapsed on Al’s watch?
9. You fly your 15 m long spaceship at a speed of 100,000 km/s relative to your friend, Rhoda Mule. Your
velocity is parallel to the ships length. How long is your spaceship as measured by Rhoda?
10. The proper (rest) lifetime of a muon is 2.20 s. If the muon has a lifetime of 34.8 s according to an
observer on Earth, what is the muon’s speed relative to the observer (as a fraction of c).
11. Alpha Centuri is about 4.30 light-years away. Suppose a spaceship traveled this distance at a constant 0.60c
relative to Earth. a) How much time would elapse on an Earth-based clock? b) How much time would elapse
on a clock on the spaceship?
12. A spaceship has a length of 150 m in its rest (proper) frame. An observer in another inertial frame measures
the length of the spaceship as 110 m. What is the relative speed of the two reference frames?
13. Two friends, Anna Grahm (age 20) and Clara Cill (age 24), say their goodbyes. Clara boards a space shuttle
for a round-trip flyby of the planet Flybymeandlivelonger. Neglecting the acceleration times, Clara returns
home 24 months later (as seen by her calendar). She is met by Anna, who is now 26 years old. At what speed
was Clara cruising?
14. Consider the passengers on board a jet cruising at 675 mph (300 m/s) with respect to an observer on the
ground. Ignoring all other effects, how long would the flight have to last for there to be a discrepancy of
1.00 s between clocks on the ground and clocks on the jet?
15. After jettisoning a stage, a rocket has a velocity of 0.20c relative to the jettisoned stage. An observer,
Meg O’Tunn, on Earth sees the jettisoned stage moving with a velocity of 0.25c relative to her and in the
same direction as the rocket. a) Using Newtonian relativity, what is the velocity of the rocket relative to Meg?
b) Using Einstein’s relativity, what is the velocity of the rocket relative to Meg?
16. A spacecraft moving away from Earth at 0.40c fires a probe back toward Earth with a speed of 0.15c
relative to the spacecraft. What is the velocity of the probe as seen by an observer on Earth?
17. A rocket launched from Earth has a speed of 0.100c relative to Earth. The rocket is headed directly toward
an incoming meteor that might hit the planet. The meteor’s speed as measured by the rocket is 0.250c. What is
the meteor’s velocity as measured by an observer on Earth?
18. Two spaceships, each with a speed of 0.60c relative to Earth, approach each other head-on. a) Using
Newtonian relativity, determine the relative speed of the ships to each other. b) What is the actual relative
speed of the ships to each other?
19. A neutron (rest mass = 1.675 x 10-27 kg) is traveling at 0.50c with respect to its target. How much
momentum does the neutron have with respect to its target?
20. A particle of mass 1.000 x 10-6 kg is fired from a device so that is has a muzzle velocity of 0.2000c with
respect to an inertial observer. Determine the rest energy, total energy and kinetic energy of the projectile with
respect to the observer.
21. A photon is to have the same total energy as a 1.00 MeV electron. What frequency must the photon have?
2. b
12. 0.68c
13. 0.94c
17. 0.154c toward Earth
21. 3.65 x 1020 Hz
3. c
4. c
5. e
6. c
7. e
8. 23 min
9. 14.1 m
10. 0.998c
11. a) 7.17 yr b) 5.73 yr
14. 1 x 1012 s or a little less than 32,000 years
15. a) 0.45 c b) 0.43c
16. 0.27c, away from Earth
18. a) 1.20c b) 0.88c
19. 2.9 x 10-19 kg m/s
20. E0 = 9 x 1010 J, E = 9.186 x 1010 J, KE = 0.186 x 1010 J
```