1. After it became clear that the Michelson-Morley Experiment was yielding a null result the physicists Lorentz and Fitzgerald (independently) suggested that the arm of the interferometer that pointed in the direction of the ether wind was being shortened by a factor . Show that this would explain the null result. (6 marks)
2. In class we derived the first half of the Lorentz Transformation equations. Your turn - please show that:

(6 marks)

3. You are judge in a high profile solar system terrorist crime. The evidence presented by the prosecution is that on April 1, 2047 an alleged terrorist (known to affiliate with the Free-the-Moon Liberation Front or FMLF) was caught on surveillance using what appears to be a hand-held communication device that under image enhancement appears to be a remote detonator. He is seen pressing a button on this device at the following spacetime coordinate: minutes (c =1). At event minutes, a tans-solar system cargo ship on route to the moon exploded. FMLF claimed responsibility for this act. Based on this information should you allow the prosecution to continue?(6 marks)
   
   
4. Show, using the Lorentz transformations that the quantity is an invariant quantity and discuss in several sentences what this means.(6 marks)
   
   
5. A Tirillian spaceship fleeing from battle passes space station DS7 at a constant velocity of 3/5 in the +x direction as seen from DS7's frame. Let this point be called Event A when the origins in both frame coincided. The Tirillians have a cloaking device making them invisible. 40 s after passing DS7 (as measured by Tirillian clocks) the Tirillians enter a dust cloud which causes the emission of an electromagnetic pulse (call this event B) which is detected by DS7. At this instant DS7 fires a photon torpedo at the Tirillian ship. Call this event C. The tirillians conclude, 80 s after passing DS7, that their entry into the cloud was likely detected and they raise their shields as a precautionary measure. Call this event D. (10 marks - 2 each)
   1. Draw or use the applet (Spacetime diagrams II) to show the worldlines of DS7 and the Tirillian ship as well as events A - D.
   2. Use Lorentz Transformations to determine when and where event B occurs in the home frame. Does the applet or your diagram show this?
   3. When does event C occur in the DS7 frame? When does event C occur in the Tirillian frame? Explain how you determined this.
   4. Which event - C or D occurs first in the DS7 frame? Which occurs first in the Tirillian frame?
   5. Is it possible that the Tirillians raised their shields because they somehow detected DS7's firing of a photon torpedo? Explain.
      
      
6. An interstellar probes leaves Earth and accelerates at a steady 1 g for 330 days . It reaches it's maximum speed and cruises at this speed for 2 years before a 330 day deceleration of 1 g. All times are measured from the Earth frame. (8 marks total)
   1. What speed did the probe reach as measured in the Earth frame? How far did the probe travel? (2 marks)
   2. Construct a spacetime diagram showing the worldline of the probe.(2 marks)
   3. How much time did this trip take as measured by the crew of their probe? (4 marks)