Two spacecraft of equal rest length (100 ns) pass very close to each other as they travel in opposite directions at a relative speed of B 3/5. The captain of ship Achilles has a laser cannon at the tail of her ship. She intends to fire the cannon at the instant that her bow is lined up with the tail of ship Beowulf. Since the Beowulf is Lorentz-contracted to 80 ns in the Achilles' reference frame, she expects the laser burst to miss the other by 20 ns (she intends the shot to be "across the bow"). However, to the observer on the Beowulf, it is the Achilles that is contracted to 80 ns. Therefore, the observer on the Beowulf concludes that if the captain of the Achilles carries out her intention, the laser burst will strike the Beowulf about 20 ns behind the bow, with disastrous consequences Sketch a picture of the two ships showing the situation that the captain of the Achilles believes (a) will occur. (b) Sketch a picture of the two ships showing the situation that the captain of the Beowulf be- lieves will occur. (c) Assume that the captain of the Achilles carries out her intentions exactly as described, ac- cording to measurements in her own frame, and analyze what really happens. Construct a carefully calibrated two-observer diagram of the situation described. Define event A to be the coincidence of the bow of the Achilles and the tail of the Beowulf and event B to be the firing of the laser cannon. Choose A to define the origin event in both frames, and locate B according to the description of the Achilles' intentions as described above. When and where does this event occur as measured in the Beowulf's frame, according to the diagram? You may assume that the ships pass each other so closely that the travel time of the laser burst between the ships is negligible. (d) Write a short paragraph describing whether the cannon burst really hits or not, according to the results you found above. Discuss the hidden assumption in the statement of the apparent paradox, and point out how one of the drawings you made in parts a) and b) is misleading

Two spacecraft of equal rest length (100 ns) pass very close to each other as they travel in opposite directions at a relative speed of B 3/5. The captain of ship Achilles has a laser cannon at the tail of her ship. She intends to fire the cannon at the instant that her bow is lined up with the tail of ship Beowulf. Since the Beowulf is Lorentz-contracted to 80 ns in the Achilles' reference frame, she expects the laser burst to miss the other by 20 ns (she intends the shot to be "across the bow"). However, to the observer on the Beowulf, it is the Achilles that is contracted to 80 ns. Therefore, the observer on the Beowulf concludes that if the captain of the Achilles carries out her intention, the laser burst will strike the Beowulf about 20 ns behind the bow, with disastrous consequences Sketch a picture of the two ships showing the situation that the captain of the Achilles believes (a) will occur. (b) Sketch a picture of the two ships showing the situation that the captain of the Beowulf be- lieves will occur. (c) Assume that the captain of the Achilles carries out her intentions exactly as described, ac- cording to measurements in her own frame, and analyze what really happens. Construct a carefully calibrated two-observer diagram of the situation described. Define event A to be the coincidence of the bow of the Achilles and the tail of the Beowulf and event B to be the firing of the laser cannon. Choose A to define the origin event in both frames, and locate B according to the description of the Achilles' intentions as described above. When and where does this event occur as measured in the Beowulf's frame, according to the diagram? You may assume that the ships pass each other so closely that the travel time of the laser burst between the ships is negligible. (d) Write a short paragraph describing whether the cannon burst really hits or not, according to the results you found above. Discuss the hidden assumption in the statement of the apparent paradox, and point out how one of the drawings you made in parts a) and b) is misleading