Your job is to synchronize the clocks in a reference frame. You are going to do so by flashing a light at the origin at t = 0 s. To what time should the clock at (x, y, z) = (30 m, 40 m, 0 m) be preset?

Carol is in the same reference frame with a clock. Bianca is flying past Carol and her clock at a high speed. Bianca sees Carol's clock ticking at one quarter the rate that Carol sees. How fast is Bianca flying relative to Carol?

652

Carl is standing in a park 1000 m across. Rohan flies over the park at a very high speed, first passing over the east end of the park, and then passing over the west end. Carl and Rohan are discussing the time interval between when Rohan passed over the east end of the park and when he passed over the west end of the park. Who measured the proper time?

496

According to Olive, her new super-speeder space yacht is

60 . 0 m

long. Lennon is on Earth watching Olive approaching at

0.964 c

. How long is Olive's space yacht according to Lennon?

537

As seen from a distant planet, ships A and B fly toward each other, with ship A having a speed of

0.91 c

. and ship B having a speed of

0.55 c

. According to the pilot of ship A, how fast is ship B approaching?

478

Bjorn is standing at x = 600 m. Firecracker 1 explodes at the origin and firecracker 2 explodes at x = 900 m. The flashes from both explosions reach Bjorn's eye at t = 3.0 μs. At what time did each firecracker explode?

582

A proton is accelerated to 0.999c. By what factor does the proton's momentum exceed its Newtonian momentum?

What are the rest energy, the kinetic energy, and the total energy of a 1.0 g particle with a speed of 0.80c?

A modest supernova (the explosion of a massive star at the end of its life cycle) releases 1.5 x 10⁴⁴ J of energy in a few seconds. This is enough to outshine the entire galaxy in which it occurs. Suppose a star with the mass of our sun collides with an antimatter star of equal mass, causing complete annihilation. What is the ratio of the energy released in this star-antistar collision to the energy released in the supernova?