Consider an "Event X," which is observed in reference frame P with spacetime coordinates (x, t) = (1500 m, 3.5 μs). Calculate the spacetime coordinates (i) of Event X in reference frame P' as it moves at a velocity of 0.90c along the positive x-axis and (ii) in reference frame P'' as it moves at a velocity of 0.90c along the negative x-axis.

As measured by observers on Earth, two stars, A and B, undergo supernovae. First, star A explodes, and 2.0 years later, a second explosion is detected from star B. A distance of 5.0 ly separates the two stars. Assume the explosion of A occurs at X_A=0 and t_A=0. Two scientific spacecraft (SC1 and SC2) are traveling from A to B at a constant velocity of 0.25c and 0.40c. When star A explodes, SC1 and SC2, positioned at the origin of their respective reference frames, coincidentally pass by A. Determine the time difference between the two explosions detected by the SC1 and SC2 crews.

While discovering Venus, two spaceships, A and B, move towards each other. A has a speed of 0.60c, and B has a speed of 0.70c with respect to Venus' reference frame. Determine the speed of A relative to B. Write your answer in terms of c.

An inertial reference frame moves at u = -0.400c in the negative x-direction (to the left) relative to a stationary frame. A detector on the inertial frame measures the speed of a moving space object to be v' to the left of the detector. Determine the speed v of the moving space object measured relative to the stationary frame when i) v' = -0.300c, ii) v' = -0.700c, and iii) v' = -0.770c

A tiny mass splits into two pieces with sufficient energy to move at speeds near the speed of light. The pieces take off in opposite directions. The speed of the particles relative to each other is 0.999c. An observer at rest on earth determines one piece to be moving at 0.800c. Find the speed of the other particle as determined by the observer.