Spaceship Malfunction. You and your team get a distress call from another ship indicating that there has been an explosion and their propulsion and navigation systems are now off line. A large piece of their ship has been jettisoned into space, and their life support systems are failing. They need help as soon as possible. You try to track them, but are only able to pick up the piece of the craft that had been projected away from them in the explosion. You look up the make and model of their ship, a Galaxy Explorer 5000 (GE 5000), which has a total mass of 49000 kg. The piece heading in your direction is the ship's storage module, and has a mass of 9500 kg. The GE 5000 was at rest with respect to your ship at the time of the explosion. (a) Assuming you received the distress call 20 minutes before the jettisoned storage module passed by your ship at a speed of 880 m/s, what is the speed of the damaged craft? (b) How far away is the Galaxy Explorer 5000 when its storage module passes by? (c) In which direction, and how fast must you go, in order to catch up with the GE 5000 before its life support systems fail. (The crew had 80 minutes of life support left when they made the distress call, so you have 60 minutes to get to them.)

Setup: A futuristic trip from Earth to Alpha Centauri is taking place. The travellers start on Earth, from position (t, x) = (0, 0). They must travel from Earth (considered stationary) to Alpha Centauri, a distance of L = 4.37 light years away, such that they arrive at Alpha Centauri at Earth time of T = 10 years. a) Team A travels with a constant acceleration so that their worldline can be parametrized by the proper time Tau as  t(Tau) = a-1sinh(a*Tau) x(Tau) = a-1(cosh(a*Tau) - 1) for a constant 'a.' They blast off at (t, x) = (0, 0) and travel with this constant acceleration until they reach Alpha Centauri at Earth time of 10 years. What proper time does Team A measure (in years)?

please answer this question.

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?