SB.5 An event occurs at t = 6.0 s and x = 4.0 s in the Home Frame. The Other Frame is moving in the +x direc- tion with x-velocity 3= 0.5 relative to the Home Frame. (a) Use a two-observer spacetime diagram to determine when and where this event occurs in the Other Frame. (b) Check your work by applying the appropriate Lorentz transformation equation.
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- Problem 1. Given two events, (x₁, t₁) and (x2, t2), use a spacetime diagram to find the speed of a frame of reference in which the two events occur simultaneously. What values may As² have in this case? Problem forongo fu odPlease derive the Lorentz transformation equations for velocities. For an object, the velocity components seen in reference frame S are: ??, ??, ??. There is a reference frame S’ is moving relative to reference frame S in the direction of +?̂. Derive ?′?, ?′?, ?′?. Please show your derivation details.a) Find the value of y for the following situation. An astronaut measures the length of his spaceship to be 100 m, while an earthbound observer measures it to be 25 m. b) What is the speed of the spaceship relative to Earth?
- 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.) |cAs spaceship A moves away from the earth at 0.490c, the captain observes a second spaceship (B) moving in the same direction at a speed of 0.482c relative to A. Find the speed of B relative to the earth. cThe 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?
- Jose is at rest in System S' that has a velocity u = +0.46c relative to system S, where Cisco is at rest. 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 = 574 m and at time t = 1.70 μs, as measured by Cisco in S. What is the x'-coordinate of the event in meters, measured by Jose in S'? Please give your answer with no decimal places.that the axes get closer to one another. 2. Prove that the "interval", defined as x² +v² + =² – c²¢ is a conserved quantity across reference frame transformations. 3. Consider two events. Give an example of coordinates x,y,z,t and x',y',z',t and relativeAt relativistic speeds near that of light, the half-life of an unstable particle moving at high speed is longer than when it is at rest. an object is longer when moving than when it is stationary. O light emitted by a moving source moves at the same speed with the same frequency. effects precede causes in some inertial frames. lengths and times only appear different and have no effect on other measurable quantities.
- Einstein concluded that the speed of light is the same in all inertial frames. Prove that the analysis of the Michelson-Morley experiment (see attached image) is in error.At relativistic speeds near that of light, the half-life of an unstable particle moving at high speed is longer than when it is at rest. O an object is longer when moving than when it is stationary. O light emitted by a moving source moves at the same speed with the same frequency. lengths and times only appear different, they are really just the same. O effects precede causes in some inertial frames.In frame o an object moves in the x-direction with velocity u = 0.82c. Find the magnitude of the x-component of the velocity in frame o' which moves at velocity v =-.75c in the x-direction relative to frame o. Give your answer in units of c (e.g. 0.703 if the answer is 0.703c). Round your answer to 3 decimal places. Add your answer