Exam 39: Relativity

Captain Ray, on the Galactic Explorer, sets off bright signal lights at the two ends of his spaceship so that they are seen as flashing simultaneously by General Kay, who is watch the ship go by. General Kay concludes that she was next to the midpoint of the ship at the instant when the lights flashed in her reference frame. This can only happen if Captain Ray, at the center of the Galactic Explorer,

Find the momentum and speed of a proton whose kinetic energy equals its rest energy. (The mass of a proton is 938.3 MeV/c²).

A spaceship leaves Earth and maintains a constant force by means of a nuclear engine. As the speed of the spaceship increases, an observer on Earth finds that relative to her the magnitude of the spaceship's acceleration is

An electron has a kinetic energy that is twice its rest energy. Determine its speed.

In a color television tube, electrons are accelerated through a potential difference of 20000 volts. With what velocity do the electrons strike the screen?

An astronaut traveling with a speed v = 0.90 c holds a meterstick in his hand. If he measures its length, he will obtain a value of

Captain Jirk reports to headquarters that he left the planet Senesca 1.88 × 10⁴ seconds earlier. Headquarters sends back the message: "Was that spaceship proper time?" It will be spaceship proper time if it was

A supertrain (rest-length = 100 m) travels at a speed of 0.950 c as it passes through a tunnel (rest-length 50.0 m). As seen by a trackside observer, is the train ever completely within the tunnel? If so, by how much?

Boat 1 goes directly across a stream a distance L and back taking a time t₁. Boat 2 goes down stream a distance L and back taking a time t₂. If both boats had the same speed relative to the water, which of the following statements is true?

A spaceship moving past the Earth with a speed of 0.800 c signals to the Earth with pulsed laser photons emitted at 10.0-second intervals according to the spaceship's clock. According to observers on Earth who see the flashes, the time interval they measure is

A 30-year-old woman takes a trip on a rocket, leaving her 20-year-old brother behind. She travels at a speed of 0.8 c, and is gone 20 years, according to the younger brother. When she returns, how many years older/younger is she than her brother?

The half-life of a muon is 2.2 μs. How fast is it moving relative to an observer who says its half-life is 4.4 μs?

A 1000-kg automobile moving with a speed of 24 m/s collides with a 500-kg car initially at rest. If the two stick together, what is the velocity (in m/s) of the two cars after the collision relative to an automobile moving in the same direction at 15 m/s?

A spaceship from another galaxy passes over the solar system directly above a radial line from the sun to the Earth. (We measure that distance to be 1.5 × 10¹¹ m.) On Earth, the spaceship is observed to be traveling at a speed of 0.80 c, for which γ = 5/3. As measured on Earth it takes the spaceship 625 seconds to travel from the sun to Earth. When a scientist in the spaceship measures the Earth-sun distance and the time it takes her to travel that distance, she finds the results are respectively

A proton has a total energy of 2.5 × 10−¹⁰ J. How fast is it moving? (M = 1.67 × 10−²⁷ kg)

A starship navigator measures the distance between the Earth and the sun. If the ship is moving at a speed of 0.90 c, instead of obtaining 93 million miles, the navigator measures a distance (in millions of miles) of

Fireworks go off at the same time according to Earth clocks in two cities, Alum and Boron, that are 300 km apart. The people in a spaceship that is flying in a straight line from Alum to Boron at 0.80 c also observe the fireworks. Do they see the fireworks in the two cities simultaneously? If the people in the spaceship say the fireworks were not simultaneous in Alum and Boron, how long before or after the fireworks flashed at Alum did the fireworks flash at Boron according to their calculations? (The spaceship is directly over Alum when the fireworks flash.)

A satellite moves east, taken as the positive x axis direction, at a speed of 0.5 c and a spaceship moves toward it (to the west) at a speed of 0.8 c as measured by an observer on the Earth. The speed of the satellite measured by an observer in the spaceship is

A spaceship moves at a speed of 0.95 c away from the Earth. It shoots a star wars torpedo toward the Earth at a speed of 0.90 c relative to the ship. What is the velocity of the torpedo relative to the Earth? (The direction in which the spaceship moves is the positive direction.)

When at rest, a spacecraft has the same height as length. When moving at relativistic speeds in the direction of its length, which one of the following describes its length and height to an observer at rest?