Exam 27: Relativity

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?

What is the momentum of a proton when it is moving with a speed of 0.60c? (m_proton = 1.67 × 10^-27 kg)

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?

If a particle has a total energy that is 5.00 times its rest energy, the speed of the particle is closest to which one of the following values?

If, instead of the correct formula for kinetic energy, we carelessly use the classical expression for kinetic energy for a particle moving at half the speed of light, by what magnitude percent will our calculation be in error? (c = 3.0 × 10⁸ m/s)

Observer A sees a pendulum oscillating back and forth in a relativistic rocket and measures its period to be T_A. Observer B moves along with the rocket and measures the period of the pendulum to be T_B. What is true about these two time measurements?

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 × 10⁹ m, and that of the orbit of Mars is 228 × 10⁹ m.

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 $26.4 \text { light-years. }$ What is the distance between the stars in their own rest frame?

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 0.82c. The commander also observes ship A, advancing in the rear, with a relative velocity of 0.50c. What is the speed of ship C as measured by the captain of ship A?

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 $0.9500 \mathrm { c } ?$ (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.

As shown in the figure, the captain of spaceship A observes spaceship E escaping with a relative velocity of 0.35c. A missile M is fired from ship A directly toward ship E, with a velocity of 0.76c relative to ship A. What does the captain of ship E measure for the velocity of the missile M?

You are a passenger on a spaceship. As the speed of the spaceship increases, you will observe

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?

A spacecraft is measured by a scientist on the ground to have a length of 81 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 length of the spacecraft? (c = 3.0 × 10⁸ m/s)

An unstable particle is moving at a speed of 1.6 × $10^8$ m/s relative to a laboratory. Its lifetime is measured by a stationary observer in the laboratory to be 6.8 × $10^{ - 6}$ s. What is the lifetime of the particle as measured in the rest frame of the particle? (c = 3.0 × 10⁸ m/s)

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?

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 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?

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.

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?