Exam 37: Relativity

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?

System has a velocity u = +0.56c relative to system S,as shown in the figure.The clocks of S and are synchronized at t = = 0 when the origins O and coincide.An event is observed in both systems.The event takes place at x = 800 m and at time t = 3.0 μs as measured by an observer in S.What is the time of the event,measured by an observer in ?

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 in the rocket,

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?

As a spaceship is moving toward Earth,an Earthling measures its length to be 325 m,while the captain on board radios that her spaceship's length is 1150 m.(c = 3.00 × 10⁸ m/s) (a)How fast is the rocket moving relative to Earth? (b)What is the TOTAL energy of a 75.0-kg crewman as measured by (i)the captain in the rocket and (ii)the Earthling?

How fast must a proton move so that its kinetic energy is 80% of its total energy?

During a nuclear reaction,the particles involved lose 4.8 × 10^-28 kg of mass.How many joules of energy are released by this reaction? (c = 3.00 × 10⁸ m/s)

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 0.78c.The commander also observes ship A,advancing in the rear,with a relative velocity of 0.31c.What is the velocity of ship C,relative to an observer on ship A?

The special theory of relativity predicts that there is an upper limit to the speed of a particle.It therefore follows that there is also an upper limit on the following properties of a particle.

In their common rest frame,two stars are 90.0 light-years (ly)apart.If they are 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.

Relative to the frame of the observer making the measurement,at what speed parallel to its length is the length of a meterstick 60 cm?

The captain of spaceship A observes enemy spaceship E escaping with a relative velocity of 0.48c,as shown in the figure.A missile M is fired from ship A,with a velocity of 0.72c relative to ship A.What is the relative velocity of approach of missile M,observed by the crew on ship E?

A proton in a certain particle accelerator has a kinetic energy that is equal to its rest energy.What is the momentum of the proton as measured by a physicist working with the accelerator? (c = 3.00 × 10⁸ m/s,m_proton = 1.67 × 10^-27 kg)

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?

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

A spaceship is moving between two distant stars at 0.932c.To someone in the ship,the distance between the two stars appears to be What is the distance between the stars in the rest frame of the stars?

How much work must be done to accelerate a particle of mass from a speed of to a speed of

A relativistic proton has a momentum of 1.0 × 10^-17 kg • m/s and a rest energy of 0.15 nJ.What is the kinetic energy of this proton? (c = 3.00 × 10⁸ m/s,m_proton = 1.67 × 10^-27 kg)

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?