3. An observer detects two explosions, one that occurs near her at a certain time and another that occurs 2.00 ms later 100 km away. Another observer finds that the two explosions occur at the same place. What time interval separates the explosions to the second observer? 4. An observer detects two explosions that occur at the same time, one near her and the other 100 km away. Another observer finds that the two explosions occur 160 km apart. What time interval separates the explosions to the second observer? 5. A spacecraft moving in the +x direction receives a light signal from a source in the xy plane. In the reference frame of the fixed stars, the speed of the spacecraft is v and the signal ar- rives at an angle to the axis of the spacecraft. (a) With the help of the Lorentz transformation find the angle e' at which the signal arrives in the reference frame of the spacecraft. (b) What would you conclude from this result about the view of the stars from a porthole on the side of the spacecraft? 12 6. A body moving at 0.500c with respect to an observer disinte- grates into two fragments that move in opposite directions rela-o tive to their center of mass along the same line of motion as the original body. One fragment has a velocity of 0.600c in the backward direction relative to the center of mass and the other has a velocity of 0.500c in the forward direction. What veloci-bol ties will the observer find? ta love o 7. A man on the moon sees two spacecraft, A and B, coming toward him from opposite directions at the respective speeds of 0.800c and 0.900c. (a) What does a man on A measure for the speed with which he is approaching the moon? For the speed with which he is approaching B? (b) What does a man on B measure for the speed with which he is approaching the moon? For the speed with which he is approaching A? 13