Exam 14: Special Relativity

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 0.83c.The commander also observes ship A,advancing in the rear,with a relative velocity of 0.48c.As measured by commander on ship B,at what speed is ship A approaching ship C?

The closest known star to our solar system is Alpha Centauri,which is approximately 4.30 light years away. A spaceship with a constant speed of 0.800c relative to the earth travels from Earth to this star. (a)How much time would elapse during the trip on a clock on board the spaceship? (b)How much time would elapse during the trip on a clock on Earth?

An unstable particle is moving at a speed of 2.6 × 10⁸ m/s relative to a laboratory. Its lifetime is measured by a stationary observer in the laboratory to be 4.7 × 10^-6 seconds.What is the lifetime of the particle,measured in the rest frame of the particle? (c = 3.00 × 10⁸ m/s)

A particle is moving at 0.75c relative to a lab on Earth.By what percentage is the Newtonian expression for its momentum in error? (The percentage error is the difference between the erroneous and correct values,divided by the correct one).

A spaceship approaching an asteroid at a speed of 0.60c launches a rocket forward with a speed of 0.40c relative to the spaceship.At what speed is the rocket approaching the asteroid as measured by an astronaut on the asteroid?

In their common rest frame,two stars are 90.0 light-years (ly)apart.If they are 12.0 ly apart as measured by the navigator in a spaceship traveling between them,how fast is the spaceship moving? Express your answer in terms of c.

Someone in Earth's rest frame says that a spaceship's trip between two planets took 10.0 y,while an astronaut on the space ship says that the trip took 6.27 y.Find the speed of the spaceship in terms of the speed of light.

System S' has a velocity u = +0.45c relative to system S,as shown in the figure.The clocks of S and S'are synchronized at t = t' = 0 when the origins O and O' coincide.An event is observed in both systems.The event takes place at x = 600 m and at time t = 1.9 μs,as measured by an observer in S.What is the x'-coordinate of the event,measured by an observer in S'?

Assume that a certain city consumes electrical energy at an average rate of 2.0 × 10⁹ W.What would be the mass change in producing enough energy to keep this city running for 21 weeks? (c = 3.00 × 10⁸ m/s)

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 0.350c to the right (both of these speeds are measured in Earth's rest frame),how fast are the particles moving with respect to each other?

Astronaut Mark Uri is space-traveling from planet X to planet Y at a speed of 0.65c relative to the planets,which are at rest relative to each other.When he is precisely halfway between the planets,a distance of 1.0 light-hour from each one as measured in the planet frame,nuclear devices are detonated on both planets.The explosions are simultaneous in Mark's frame.What is the difference in the time of arrival of the flashes from the explosions as observed by Mark?

An astronaut on a spaceship moving at 0.927c says that the trip between two stationary stars took 7)49 y.How long does this journey take as measured by someone at rest relative to the two stars?

A spaceship approaches the earth with a speed 0.50c.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 the earth?

During a nuclear reaction,1.7 × 10^-4 J of energy is released. What is the resulting change in mass of the particles involved? (c = 3.00 × 10⁸ m/s)

Consider three galaxies,Alpha,Beta and Gamma.An observer in Beta sees the other two galaxies each moving away from him in opposite directions at speed 0.70c.At what speed would an observer in Alpha see the galaxy Beta moving?

A spacecraft is measured by an observer on the ground to have a length of 53 m as it flies toward the earth with a speed 1.7 × 10⁸ m/s.The spacecraft then lands and its length is again measured by the observer on the ground,this time while the spacecraft is at rest on the launchpad. What result does he now get for the length? (c = 3.00 × 10⁸ m/s)

An astronaut leaves Earth in a spaceship at a speed of 0.960c relative to an observer on Earth.The astronaut's destination is a star system 14.4 light-years away (one light-year is the distance light travels in one year.)According to the astronaut,how long does the trip take?

A rocket is moving at 1/4 the speed of light relative to Earth.At the center of this rocket,a light suddenly flashes.To an observer at rest on Earth

A spaceship is moving away from the earth with a constant speed of 0.80c. The spaceship fires a 28-kg missile with a speed of 0.50c relative to the spaceship.What is the speed of the missile measured by observers on the earth if the missile is fired (a)away from the earth? (b)toward the earth?

Two spaceships are approaching one another,each at a speed of 0.28c relative to a stationary observer on Earth.What speed does an observer on one spaceship record for the other approaching spaceship?