Answer Happy

Question 4 (marks: 2+4+3+1 = 10) Sam and Eve are twins. At age 10 years Sam leaves Eve on Earth in a spaceship travelling at 0.5c. At age 40 years Eve sets off after Sam in a spaceship travelling at 0.9c. (a) Draw a Minkowski spacetime diagram showing the world-lines of Sam and Eve from the events of Sam leaving the Earth to the event M of their meeting again. Let E be the event of Eve leaving Earth. Clearly mark the events S, M and E on your diagram. (HINT: Drawing the diagram properly is the key to this problem. Don't forget that time flows forward!) (b) Let 0, be the angle between the world-lines of Sam and the Earth and and $2 is that of between Eve and the Earth. Find the lengths of the intervals SM and EM. (HINT: You might find it useful to draw a perpendicular line from the world-line of the Earth to the event M.) (c) When Sam and Eve meet (at event M) who is the older? (d) What is the age difference in (c)?