1. Two ships make a trip from the planet Melmack to the planet Ork. The red ship makes the trip at a speed of 0.35c relative to the planets. The blue ship makes the trip at a speed of 0.48c relative to the planets, and while traveling, its science officer measures the distance between the planets to be 17 light-years. a) What is the proper length of the trip between these planets? b) Find the length (in light-years) the red ship's science officer measures the trip to be, as they travel. 2. Two events occur. Juan measures a time interval between the events of Δt=3.5 yrs and a distance between the events Δx=2.2 light-years. a) Find the space-time interval Δs2. b) Is this interval space-like, time-like, or light-like? c) Will any observer observe the events as simultaneous? If so, how does that observer move relative to Juan? If not, prove it. 3. A ruby laser at rest would emit light of wavelength 694 nm. You observe a moving ruby laser to emit light of wavelength 702 nm. a) Is the laser moving toward you or away from you? b) How fast? 4. A Borg spaceship is on its way to Earth. A Federation spaceship is sent from Earth at a speed of 0.9c to intercept it. The speed of the Borg ship relative to the Federation ship is 0.95c. a) Draw a diagram, and label a positive direction. b) What is the speed and direction of the Borg ship relative to the Earth? Does anyone have any idea about these four problems. One of these is going to be on my exam tomorrow. I'll be really and infact a million times thankful to anyone who helps me with these problems soon. very soon please because I'm not good in physics. I really need to do this exam good. Please somebody help!!!
How are the ships and planets aligned ? This is needed to solve the problems. The answers can be found by applying the relativistic formulae you got in your notes or text book. If the blue ship is lined up with the planets, the distance between them as measured from the blue ship is given by the 'length contraction' formula. Look this up.