System S' has a velocity u = +0.31c 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 = 654 m and at time t = 1.8 μs, as measured by an observer in S. What is the x'-coordinate of the event, measured by an observer in S'?

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.

Rockets A and C move with velocities +0.85c and -0.75c with respect to B, who is at rest in this frame of reference. A rod in rocket A has length L. What is the length of the rod according to an observer in rocket C?

Observers 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-s

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 Xm

A 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?

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?