The origins of two frames coincide at t = t = 0 and the relative speed is 0.976c. Two micrometeorites collide at coordinates x = 85.2 k and t = 260 us according to an observer in frame S. What are the (a) spatial and (b) temporal coordinate of the collision according to a observer in frame 5? (a) Number Units (b) Number Units
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and t= 260 us according to an observer in frame S. What are the (a) spatial and (b) temporal coordinate of the collision according to an
observer in frame 5?
(a) Number
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Units
(b) Number
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- Electromagnetic radiation from a star is observed with an earth-based telescope. The star is moving away from the earth with a speed of 0.590c. If the radiation has a frequency of 8.64 x 10 Hz in the rest frame of the star, what is the frequency measured by an observer on earth? a) Of = 4.39 x 1014 Hz b) Of = 4.93 x 1014HZ c)Of = 4.45 x 1014 Hz d) Of = 4.39 x 1015 Hz e) Of = 4.69 x 1014 HzThe origins of two frames coincide at t = t' = 0 and the relative speed is 0.961c. Two micrometeorites collide at coordinates x = 129 km and t = 192 μs according to an observer in frame S. What are the (a) spatial and (b) temporal coordinate of the collision according to an observer in frame S'?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 = ? s
- The origins of two frames coincide at t = t' = 0 and the relative speed is 0.968c. Two micrometeorites collide at coordinates x = 139 km and t = 234 μs according to an observer in frame S. What are the (a) spatial and (b) temporal coordinate of the collision according to an observer in frame S'?An observer moving at a speed of 0.995c relative to a rod (see figure below) measures its length to be x = 2.20 m and sees its length to be oriented at 0 = 33.0° with respect to its direction of motion. x Ꮎ Motion of observer (a) What is the proper length of the rod? m (b) What is the orientation angle in a reference frame moving with the rod? O1. A spaceship A (at rest in inertial frame A) of proper length L, =75.0m is moving in the +x direction at a speed v= 0.650c as measured in the Earth frame. Another spaceship B (at rest in inertial frame B) is moving on a parallel path in the opposite direction (-x) with u, =-0.720c as measured in the Earth frame. The two spaceships pass each other. a. What is the velocity and speed parameter of spaceship B in inertial frame A, u,,B' ? b. In inertial frame A, how long does it take for the tip of spaceship B to move from the tip of spaceship A to the tail of spaceship A? c. In inertial frame B, how long does it take for the tip of spaceship B to move from the tip of spaceship A to the tail of spaceship A? d. In the Earth frame, how long does it take for the tip of spaceship B to move from the tip of spaceship A to the tail of spaceship A?
- 1. You are an observer in a 100-m long spacecraft traveling from the earth to the moon at 0.8c. (a)What is the proper length of the spacecraft? (b) For a proper time interval of 1 sec., the relativistic time interval for the spacecraft measured from the earth reference frame would be: (c)Time dilation does not apply to all time-dependent physical and biological processes. T/F? (c) What is the relativistic length, DL measured from the reference frame of earth? (d) An APOLLO crew left a flat mirror reflector on the surface of the moon (for all you deniers out there, in the 50th anniversary year of APOLLO 11!). If the average surface-to-surface distance from the earth to the moon is 3.83 x 10^8 m, then how long does it take moonlight to reach earth?Chapter 37, Problem 012 The length of a spaceship is measured to be exactly 1/2 its rest length. (a) What is the speed parameter ß of the spaceship relative to the observer's frame? (b) By what integer factor do the spaceship's clocks run slow, compared to clocks in the observer's frame? (a) Number Units (b) Number UnitsIn frame S, event B occurs 2 ms after event A and at Dx = 1.5 km from event A. (a) How fast must an observer be moving along the +x axis so that events A and B occur simultaneously? (b) Is it possible for event B to precede event A for some observer?(c) Draw a spacetime diagram that illustrates your answers to (a) and (b). (d) Compute the spacetime interval and proper distance between the events.
- System S' has a velocity u = +0.33c relative to system S, as shown in the figure. The clocks of S and S' are synchronized at t = t' = 0 when the origins O and O' coincide. An event is observed in both systems. The event takes place at x = 672 m and at time t = 1.6 μs, as measured by an observer in S. What is the x'-coordinate of the event, measured by an observer in S'?A certain type of elementary particle travels at a speed of 2.53 x 108 m/s relative to a lab. The average lifetime in the particle's rest frame is calculated to be 62.6 us. What will be the lifetime of the particle (in us) as measured by someone in the lab? (Use c = 2.9979 × 108 m/s)Earth and a star are 20 light years (ly) apart, measured in a frame at rest with respect to Earth and star. Twin A boards a spaceship, travels at 0.80c to the star, and then returns immediately to Earth at 0.80c. Determine the round-trip travel times in Earth and ship refer- ence frames.