Exam 29: Relativity

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?

Observer A sees a ruler moving by in a relativistic rocket and measures its length to be L_A.Observer B moves along with the rocket and measures the length of the ruler to be L_B.What is true about these two length measurements?

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?

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 What is the distance between the stars in their own rest frame?

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 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 space barge pushes on a spaceship with a rest mass of 15,000 kg and accelerates it from a speed of 0.600c to a speed of 0.700c.How much work does the barge have to do to accomplish this? (c = 3.00 × 10⁸ m/s)

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?

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 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?

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 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 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?

If the kinetic energy of a proton is 80% of its total energy,what is the speed of the proton?

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 long did it take for the spaceship to travel that distance? The radius of the orbit of Jupiter is 778 × 10⁹ m,and that of the orbit of Mars is 228 × 10⁹ m.

A 1.00-kg gold ingot is carried from the bottom of the Eiffel tower to the top,300 m above ground level.By what amount does its mass change? (c = 3.00 × 10⁸ m/s)

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 satellite,initially at rest in deep space,separates into two pieces,which move away from each other.One piece has a rest mass of 190 kg and moves away with a speed 0.280c,and the second piece moves in the opposite direction with a speed 0.600c.What is the rest mass of the second piece?

Calculate the speed at which a 0.723-kg object has the same momentum as a 1.30-kg object that is moving 0.515c.

In a nuclear plant,10¹⁷ J of energy is available from mass conversion.How much mass of fuel was lost to produce this energy? (c = 3.0 × 10⁸ m/s)