Concept explainers
(a)
The speed of the laser beam registered by the second ship’s personnel according to the classical addition of the velocities, if you are on a spaceship traveling at
(b)
The speed of the laser beam registered by the second ship’s personnel according to the relativistic addition of the velocities if you are on a spaceship traveling at
(c)
The speed of the second ship with respect to yours according to the classical addition of the velocities, if you are on a spaceship traveling at
(d)
The speed of second ship with respect to your spaceship according to the relativistic addition of the velocities, if you are on a spaceship traveling at
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College Physics
- Suppose a spaceship heading straight towards the Earth at 0.750c can shoot a canister at 0.500c relative to the ship. (a) What is the velocity of the canister relative to the Earth, if it is shot directly at the Earth? (b) If it is shot directly away from the Earth?arrow_forwardA muon formed high in the Earths atmosphere is measured by an observer on the Earths surface to travel at speed = 0.990c for a distance of 4.60 km before it decays into an electron, a neutrino, and an antineutrino (c+v+v). (a) For what time interval does the muon live as measured in its reference frame? (b) How far does the Earth travel as measured in the frame of the muon?arrow_forward(a) Find the kinetic energy of a 78.0-kg spacecraft launched out of the solar system with speed 106 km/s by using the classical equation K=12mu2. (b) What If? Calculate its kinetic energy using the relativistic equation. (c) Explain the result of comparing the answers of parts (a) and (b).arrow_forward
- A pulsar is a stellar object that emits light in short bursts. Suppose a pulsar with a speed of 0.950c approaches Earth, and a rocket with a speed of 0.995c heads toward the pulsar. (Both speeds are measured in Earth's frame of reference.) If the pulsar emits 10.0 pulses per second in its own frame of reference, at what rate are the pulses emitted in the rockets frame of reference?arrow_forwardTwo identical spaceships with proper lengths of 175 m are launched from Earth. Spaceship A is launched in one direction at 0.500c and spaceship B is launched in the opposite direction at 0.750c. (a) What is the speed of spaceship B relative to spaceship A? (b) What is the length of spaceship A as measured by astronauts on spaceship B?arrow_forwardSuppose a spaceship heading straight toward the at 0.750c can shoot a canister at 0.500c relative to the ship. (a) What is the velocity of the canister relative to Earth, if it is shot directly at Earth? (b) If it is shot directly away from Earth?arrow_forward
- An astronaut is traveling in a space vehicle moving at 0.500c relative to the Earth. The astronaut measures her pulse rate at 75.0 beats per minute. Signals generated by the astronauts pulse are radioed to the Earth when the vehicle is moving in a direction perpendicular to the line that connects the vehicle with an observer on the Earth. (a) What pulse rate does the Earth-based observer measure? (b) What If? What would be the pulse rate if the speed of the space vehicle were increased to 0.990c?arrow_forwardSuppose the observer O on the train in Figure 38.6 aims her flashlight at the far wall of the boxcar and turns it on and off, sending a pulse of light toward the far wall. Both O and O measure the time interval between when the pulse leaves the flashlight and when it hits the far wall. Which observer measures the proper time interval between these two events? (a) O (b) O (c) both observers (d) neither observer Figure 38.6 (a) A mirror is fixed to a moving vehicle, and a light pulse is sent out by observer O at rest in the vehicle. (b) Relative to a stationary observer O standing alongside the vehicle, the mirror and O move with a speed v and the light pulse follows a diagonal path. (c) The right triangle for calculating the relationship between t and tp.arrow_forwardUnreasonable Results A spaceship is heading directly toward the Earth at a velocity of 0.800c. The astronaut on board claims that he can send a canister toward the Earth at 1.20c relative to the Earth. (a) Calculate the velocity the canister must have relative to the spaceship. (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?arrow_forward
- A spacecraft built in the shape of a sphere moves past an observer on the Earth with a speed of 0.500c. What shape does the observer measure for the spacecraft as it goes by? (a) a sphere (b) a cigar shape, elongated along the direction of motion (c) a round pillow shape, flattened along the direction of motion (d) a conical shape, pointing in the direction of motionarrow_forwardAn alien spaceship traveling at 0.600c toward the Earth launches a landing craft. The landing craft travels in the same direction with a speed of 0.800c relative to the mother ship. As measured on the Earth, the spaceship is 0.200 ly from the Earth when the landing craft is launched. (a) What speed do the Earth-based observers measure for the approaching landing craft? (b) What is the distance to the Earth at the moment of the landing crafts launch as measured by the aliens? (c) What travel time is required for the landing craft to reach the Earth as measured by the aliens on the mother ship? (d) If the landing craft has a mass of 4.00 105 kg, what is its kinetic energy as measured in the Earth reference frame?arrow_forwardIf astronauts could travel at v = 0.950c, we on Earth would say it takes (4.20/0.950) = 4.42 years to reach Alpha Centauri, 4.20 light-years away. The astronauts disagree. (a) How much time passes on the astronauts clocks? (b) What is the distance to Alpha Centauri as measured by the astronauts?arrow_forward
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