35. Special Relativity

Lorentz Transformations

Open Question
An event has spacetime coordinates (x,t) = (1200 m, 2.0 μs) in reference frame S. What are the event's spacetime coordinates (a) in reference frame S' that moves in the positive x-direction at 0.80c and (b) in reference frame S'' that moves in the negative x-direction at 0.80c?
Multiple Choice
In a lab frame, S, an object crosses a distance of 15 m in 10 s. In an initially aligned frame S', moving at 1000 km/s in the x-direction relative to S, how far a distance does the object have to travel, and in what time does it travel the distance?
Multiple Choice
In a particle accelerator, a neutron is traveling at a speed of 0.7 c, as measured by you in a laboratory. This neutron decays (becoming a proton), ejecting an electron. If you measure the electron's speed to be 0.5 c, traveling in the same direction as the neutron, what was the relative speed between the electron and neutron when the neutron decayed? Was the electron ejected forward or backwards relative to the neutron's motion, as 'seen' by the neutron?
Multiple Choice
According to Earth-based observers, the space time coordinates of a collision between two asteroids are $(x, t) = (3.0 \times 10^{11} m, 450 s)$ . What are the coordinates according to an astronaut moving in the positive x direction at 0.78c $0.78 c$ ?
Multiple Choice
What is the momentum of a proton moving at $0.987 c$ ?
Multiple Choice
For a particle moving $0.954 c$ . what percent of its total energy is kinetic energy?
Open Question
Two rockets approach each other. Each is traveling at 0.75c in the earth's reference frame. What is the speed, as a fraction of c, of one rocket relative to the other?
Open Question
An observer in frame S′ is moving to the right 1+x-direction2 at speed u = 0.600c away from a stationary observer in frame S. The observer in S′ measures the speed v′ of a particle moving to the right away from her. What speed v does the observer in S measure for the particle if (a) v′ = 0.400c; (b) v′ = 0.900c; (c) v′ = 0.990c?
Open Question
A pursuit spacecraft from the planet Tatooine is attempting to catch up with a Trade Federation cruiser. As measured by an observer on Tatooine, the cruiser is traveling away from the planet with a speed of 0.600c. The pursuit ship is traveling at a speed of 0.800c relative to Tatooine, in the same direction as the cruiser. (a) For the pursuit ship to catch the cruiser, should the velocity of the cruiser relative to the pursuit ship be directed toward or away from the pursuit ship? (b) What is the speed of the cruiser relative to the pursuit ship?
Open Question
Two particles are created in a high-energy accelerator and move off in opposite directions. The speed of one particle, as measured in the laboratory, is 0.650c, and the speed of each particle relative to the other is 0.950c. What is the speed of the second particle, as measured in the laboratory?