= An observer at origin of inertial frame S sees a flashbulb go off at x = 190km, y 20km, and z = 0km at time t = 5 x 10-4s. At what time and position in the S' system did the flash occur, if S' is moving along shared x-direction with S at a velocity v = 0.8c? Let the origins of frame S and frame S' coincide at time t = 0 and t'= 0. Hint The time (in units of 10-4s) and position (in units of km) of the flash is [Format hint: Specify your answer as a 4-tuple, for example, (2, 100, 5, 1), for a flash occurring at 2 x 10-s at the location of (x = 100km, y = 5km, z = 1km).]

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.

An experimenter has studied the decay of a K° particle in which it emits a 7° at 0.8c. One such K° particle passes the experimenter at 0.5c and decays, emitting a 7° in the original direction of motion. In the experimenter's frame, the speed of the T° is measured to be O 1.3c. O between c and 1.3c. between .5c and .8c. O between .8c and c..

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?

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.

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?

You and vouur archenemy pass each other in rockets that are each traveling 0.2c relative to the other. You observe that your rocket (which you have measured to be 281 m Jong ten times as long as your archenemy's spaceship. How long is your rocket in your archenemy's frame? How long is your archenemy's rocket in their frame?

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 results