For the twins Frank and Mary described in Section 2.8, consider Mary's one-way trip at a speed of 0.8c to the star system 8 lightyears from Earth. Compute the spacetime interval As² in the fixed frame and As'2 in the moving frame and compare the results.
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- In 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.A spaceship leaves the solar system at v = (3/5)c and is headed towards a planet that is 20 c • years away (c is the speed of light). Assume the following: the Sun and the planet are mutually at rest and their clocks have been synchronized such that both read zero when the spaceship leaves. Say that the clock on the ship began at zero. If this is the case, then what should the clock on the ship read when it arrives at the planet?The proper length of one spaceship is three times that of another. The two spaceships are traveling in the same direction and, while both are passing overhead, an Earth observer measures the two spaceships to have the same length. If the slower spaceship has a speed of 0.354c with respect to Earth, determine the speed of the faster spaceship. (Give your answer to at least 3 significant figures.) |c
- An object is moving with ordinary speed 0.5c in S reference frame along a direction making an angle (tan 9 = 2) with respect to the positive x - axis. Find the zeroth component of the proper velocity.1) Calculate the interval As 2 between two events with coordinates (x1 = 50 m, y1 = 0, z1 = 0, t1 = 1 us) and (x2 = 120 m, y2 = 0, z2 = 0, t2 = 1.2 µs) in an inertial frame S. 2) Now transform the coordinates of the events into the S0 frame, which is travelling at 0.6c along the x-axis in a positive direction with respect to the frame S. Hence verify that the spacetime interval is invariant.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?
- Determine an expression for the total travel time of the light pulse, as measured by the following: A) an observer in the S frame (Use the following as necessary: c, d, and v.) B) an observer on the spacecraft (Use the following as necessary: c, d, and v.) What If? If the transmitted light beam has a wavelength λT, determine an expression for the shift in the wavelength of the light beam, as measured by the following C) an observer in the S frame (Use the following as necessary: c, v, and λT.) D) an observer on the spacecraft (Use the following as necessary: c, v, and λT.)In the Marvel comics universe, Quicksilver is awfully fast. Let's say he can run at a velocity of 0.56c. He measures a trip as having a distance of 4.60e+05 m. How much time does Quicksilver measure this trip as taking? 2.73e-3 S Does Quicksilver measure the proper or dilated time? 2 proper time v Quicksilver's sister, Wanda Maximoff, is standing stationary near where he is running. How much time does Wanda measure this trip as taking? 3 3.29e-3 S What distance does Wanda measure for Quicksilver's trip? 4 XmA person on Earth observes two rocket ships moving directly toward each other and colliding as shown in the figure below. At time t = 0 in the Earth frame, the Earth observer determines that rocket A, travelling to the right at vA = 0.80c, is at point a, and rocket B is at point b, travelling to the left at vB = 0.60c. According to the Earth observer they are separated by a distance l = 4.2 x 108 m as shown in the other figure. How much time will elapse in frame A from the time rocket A passes point auntil collision?
- A rocket measures 100 m long in its own frame (S') and is travelling at 0.995c relative to a frame S. At the tail of the rocket, a laser sends out a pulse of light which is reflected by a mirror at the nose of the rocket. (a) At what time after emission, measured in S', does the light pulse arrive back at the tail of the rocket? (b) At what time after emission, measured in S, does the light pulse arrive back at the tail of the rocket? (c) What is the spatial distance, measured in S, between the emis- sion of the pulse and its arrival back at the tail of the rocket? (d) At what time after emission, measured in S, does the light pulse hit the mirror? (e) What is the spatial distance, measured in S, between the emis- sion of the pulse and its hitting the mirror? (f) Can you conclude from your answers that the light pulse travelled at a different speed, as seen in S, on its way to the mirror than on the way back? If not, explain your resultsI am currently working through a physics book (Spacetime Physics by Edwin Taylor) and I have come across this question and I don't know how to solve it: "Take the differential of this equation for g to obtain an approximate algebraic expression for Δg, the change in g, for a small change Δr in height." How do I sovle this question?