Z1 is a star system that is 11.90 light-years away from Earth. Astronauts in an advanced space ship travel from Earth to Z1 at high speed, and they age only 6.50 years during the journey. (a) How fast were the Astronauts travelling? (b) The ship was launched from Earth by turning trash into 100% energy. How much trash must have been converted into energy to launch the 2.0 x 109 kg ship to this speed?

Quasars are faint, distant sources of radio waves. (Quasar is short for "quasi-stellar source." They are so named because, like a star, they appear to the astronomer to be pointlike.) From the shift in the frequency of their emitted light toward the red, called the "redshift," we know that quasars are moving very fast. Astronomers observe that the more distant an object is from the earth, the faster it moves. In this way they determine that quasars are billions of light years from earth. To be visible at this great distance, quasars must have enormous luminosity. Typically a quasar radiates energy at a rate on the order of 1040 W, roughly 1014  times greater than the sun or 40 times greater than the most luminous galaxy. At what rate is rest mass being consumed to produce this much radiation?

The cosmic rays of highest energy are protons that have kinetic energy on the order of 1o13 Mev. (a) As measured in the proton's frame, what time interval would a proton of this energy require to travel across a galaxy which has a proper diameter 7.80 × 104 ly? (Assume the kinetic energy of the proton is exactly 1013 Mev.) (b) From the point of view of the proton, how many kilometers across is the galaxy? km

If a m = 81.1 kg person were traveling at v = 0.980c, where c is the speed of light, what would be the ratio of the person's relativistic kinetic energy to the person's classical kinetic energy? kinetic energy ratio: What is the ratio of the person's relativistic momentum to the person's classical momentum? momentum ratio:

The Starship Enterprise, according some Trekkie analysts, is 300 meters long. If it is traveling at 0.985c. what would be the value of L, its length as seen from Earth?

An alpha particle is the nucleus of a He-4 atom and has a rest mass of 3727.38 MeV/c2. How much energy is required to accelerate an alpha particle from rest to 0.6c? What is the momentum of the alpha particle once it reaches this speed? Would more, less or the same amount of energy be required to accelerate a proton from rest to this speed?

What is the kinetic energy of an electron if its speed is 0.992c?

If astronauts could travel at  v = 0.956c,  we on Earth would say it takes  (4.20/0.956) = 4.39  years to reach Alpha Centauri, 4.20 light-years away. The astronauts disagree. (a) How much time passes on the astronauts' clocks? years(b) What is the distance to Alpha Centauri as measured by the astronauts? light-years

The proper lifetime of a certain particle is 100.0 ns. How long does it live in the laboratory if it moves at v = 0.860c?

You are an astronaut traveling at 75% the speed of light. It would require you 25 years as measured by Earth observers to make a round trip to a nearby star. How many years would you age during the trip?