In the laboratory inertial frame, which we assume to be inertial, two events occur simultaneously at a distance of 3 m apart in the x-direction. In another inertial frame moving with respect to the x-direction of the laboratory frame, one event occurs later than the other by 10-8 s. By what spatial distance are the two events separated in the moving frame? Assume that the value of the speed of light is c = 3 x 108 m/s. Select one: O a. 3 m O b. 3√2m O c. 6 m O d. 2√3 m
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- Chapter 37, Problem 025 = 780 m. As detected by observer S', the two flashes Observer S detects two flashes of light. A big flash occurs at x1 = 1390 m and, 5.13 µs later, a small flash occurs at x2 occur at a single coordinate x'. (a) What is the speed parameter of S', and (b) is S' moving in the positive or negative direction of the x axis? To S', (c) which flash occurs first and (d) what is the time interval between the flashes? (a) Number Units (ь) (c) (d) Number UnitsThe origins of two frames coincide at t = ť = 0 and the relative speed is 0.976c. Two micrometeorites collide at coordinates x = 85.2 km 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 i Units (b) Number i UnitsAn astronaut is traveling at a constant velocity of 0.8 times the speed of light (c = 3 x 10^8 m/s) away from a space station. If the astronaut's clock is ticking normally, but the space station observes their clock to be running slower due to time dilation, calculate the time interval experienced by the astronaut during a 1-hour period according to their own clock.
- The fastest spacecraft ever launched was the Helios probe, which travelled approximately 70,000 m/s as it passed close to the Sun. The speed of light is 3x 10^8 m/s. Suppose the Helios probe passed by a stationary observer on Earth. The observer can see an accurate clock ticking on the side of the Helios Probe.How many seconds on Earth are equivalent to one second on the Helios probe?A relativistic proton has a momentum of 1.0 × 10-17 kg ∙ m/s and a rest energy of 0.15 nJ. What is the kinetic energy of this proton? (c = 3.00 × 108 m/s, mproton = 1.67 × 10-27 kg)The space and time coordinates for two events as measured in a frame S are as follows: Event 1: x1=x0 , t1=x0/c Event 2: x2=2x0, t2=x0/2c a. There exists a frame in which these events occur at the same time. Find the velocity of this frame with respect to S. b. What is the value of t at which both events occur in the new frame?
- A particle is accelerated from 0.975c to 0.992c as measured in a laboratory reference frame. This is a change in speed of only 1.7% and the ratio of the velocities is 1.017 (as measured in the lab frame). What is the ratio of the particle momentum when moving at 0.992c as compared to when it was moving at 0.975c? This ratio should be expressed as a decimal number. P2 P₁Observers in reference frame S see an explosion located at x1=620 m. A second explosion occurs 6.0 micro-s later at x2=1500 m.In reference frame S', which is moving along the +x-axis at speed V, the explosions occur at the same point in space. What is the separation in time delta t' between the two explosions as measured in frame S'? Express your answer in microseconds (micro-s). delta t' = ? micro-sThe distance to a particular star, as measured in the earth's frame of reference, is 7.11 light- years (1 light-year is the distance that light travels in 1 y). A spaceship leaves the earth and takes 3.35 y to arrive at the star, as measured by passengers on the ship. (a) How long does the trip take, according to observers on earth? (b) What distance for the trip do passengers on the spacecraft measure?
- The muon is an unstable particle that spontaneously decays into an electron and two neutrinos. In a reference frame in which the muons are stationary, if the number of muons at t = 0 is N0, the number at time t is given by , where τ is the mean lifetime, equal to 2.2 ms. Suppose the muons move at a speed of 0.95 c and there are 5.0 × 104 muons at t = 0. (a) What is the observed lifetime of the muons? (b) How many muons remain after traveling a distance of 3.0 km?The inertial reference frames, S and S', both share the same origin at t =t'=0. The S' frame is moving at a speed 0.700c in the positive direction, as seen by frame S. An event happens at (t',x', y', z') (300s, 2.50x10"m, 1.50x10"m, 2.90x10"m), as observed in the S' frame. What are the spacetime coordinates in the S frame?A particle zips by us with a Lorentz factor of 1.12. Then another particle zips by us moving at twice the speed of the first particle. (a) What is the Lorentz factor of the second particle? (b) If the particles were moving with a speed much less than c, the magnitude of the momentum of the second particle would be twice that of the first. However, what is the ratio of the magnitudes of momentum for these relativistic particles?