A spaceship whose rest length is 406 m has a speed of 0.83c with respect to a certain reference frame. A micrometeorite, also with a speed of 0.83c in this frame, passes the spaceship on an antiparallel track. How long does it take this object to pass the spaceship as measured on the ship?
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- Twins who are 19.0 years of age leave the earth and travel to a distant planet 12.0 light-years away. Assume that the planet and earth are at rest with respect to each other. The twins depart at the same time on different spaceships. One twin travels at a speed of 0.905c, and the other twin travels at 0.407c. (a) According to the theory of special relativity, what is the difference between their ages when they meet again at the earliest possible time? A₂-A₁ = (b) Which twin is older?Spaceship A moves past the earth at 0.85 c to the west. Spaceship B approaches A, moving to the east. Both spaceship crews measure their relative speed of approach to be 0.950 c., What mass would the crews of both spaceships measure for the standard kilogram, kept at rest on the earth, according to the special theory of relativity?The inertial reference frames, S and S', both share the same origin at t = t'= 0. The 5' trame is moving at a speed 0.700c in the positive direction, as seen by frame S. An event happens at (1', x', y', z') = (300s, 2.50×10m,1.50×10"m, 2.90x10"m), as observed in the S' frame. What are the spacetime coordinates in the S frame?
- a) Galactus tries to destroy the Earth by stopping the Moon in its orbit. What effect would this have on the Moon and on the Earth? b) To prevent this, Flash (sorry, wrong company) runs to the Moon at a speed of 0.998c. From his point of view, the trip takes 0.126 s. How long does it take from our point of view on Earth?An observer in reference frame S' observes that a lightning bolt strikes the origin, and 1.0×10−4 s later a second lightning bolt strikes the same location. What is the time separation delta t between the two lightning bolts determined by a second observer in reference frame S moving at a speed of 0.90c along the collinear x-x'-axis? delta t = ? sA spaceship moves past Earth with a speed of 0.808c. As it is passing, a person on Earth measures the spaceship's length to be 78.7 m. HINT (a) Determine the spaceship's proper length (in m). m (b) Determine the time (in s) required for the spaceship to pass a point on Earth as measured by a person on Earth. s (c) Determine the time (in s) required for the spaceship to pass a point on Earth as measured by an astronaut onboard the spaceship. s
- 1. Consider inertial reference frame S to be the lab frame. A proton is moving in the positive x (+x) direction at a kinetic energy of 1250 MeV, as measured in frame S. Inertial reference frame S' moves at a speed of 0.55c in the positive-x (+x) direction relative to frame S. a) Find the speed of the proton in terms of the speed of light, c, as measured in frame S. b) Find the magnitude and direction of the speed of the proton as measured in frame S'.A rocket launched outward from Earth has a speed of 0.38c relative to the Earth. The rocket is directed toward an incoming meteor that may hit the planet. If the meteor moves with a speed of 0.70c relative to the rocket and directly toward it, what is the speed of the meteor as observed from Earth?A spacecraft has a speed of 0.4c relative to Earth. As measured on Earth, the elapsed time between two events that happen at the same location on Earth is 4 h. Determine what the elapsed time between those two events would be from the spacecraft's frame.
- Twins who are 19.0 years of age leave the earth and travel to a distant planet 12.0 light-years away. Assume that the planet and earth are at rest with respect to each other. The twins depart at the same time on different spaceships. One twin travels at a speed of 0.867c, and the other twin travels at 0.515c. (a) According to the theory of special relativity, what is the difference between their ages when they meet again at the earliest possible time? A₂-A₁ = i (b) Which twin is older?An alien spaceship traveling at 0.560c toward the Earth launches a landing craft. The landing craft travels in the same direction with a speed of 0.760c relative to the mother ship (as measured by aliens on the mother ship). As measured on the Earth, the spaceship is 0.130 ly from the Earth when the landing craft is launched. (a) What speed do the Earth-based observers measure for the approaching landing craft? 0.926 C (b) What is the distance to the Earth at the moment of the landing craft's launch as measured by the aliens (mother ship)? 0.108 ly (c) What travel time is required for the landing craft to reach the Earth as measured by the aliens on the mother ship? 0.19 Your response differs from the correct answer by more than 100%. yr (d*) What travel time is required for the landing craft to reach the Earth as measured by Earth-based observers? yr (e*) What travel time is required for the landing craft to reach the Earth as measured by those on the landing craft? yrSuppose a cosmic ray colliding with a nucleus in the Earth's upper atmosphere produces a muon that has a velocity v= 0.980c. The muon then travels at constant velocity and lives 1.52 us as measured in the muon's frame of reference. (You can imagine this as the muon's internal clock. See the figure below. Enter your answers to at least four significant figures. Assume the speed of light is 2.998 x 108 m/s.) اد us At (a) How long (in us) would the muon have lived as observed on the Earth if its velocity was 0.0690c? (b) How far (in m) would it have traveled as observed on the Earth? (c) What distance (in m) is this in the muon's frame?