Question

) You are working on a Physics NYC lab involving lasers while travelling on your superfast spaceship headed towards Mars. Assume that Mars is 300 million km (3.00 x1011 m) away from Earth (according to Earth) and that you must make it to Mars and back in exactly 2.00 hours (also according to Earth) since this is still the allotted lab time. a) How fast are you travelling (according to Earth) in terms of the speed of light, c?

Answer 1

Solution : the question, in to earth's frame According of mars and earth, no = 3 X x 101 m distance to mes and time to travel from earth earth tó again to back 2 houng = 2X3600 second = 7200 seconds. consider V be the let VS Now, of Spaceship velocity time dialation ime taken time from Now, frame, in trip spaceship ton the to t VI-VI cz frame is v earth in velocity Now, given by total time distance 2ko t v v 2.ro to V-vez 206. - - Va to 12 426² t² 2 to 426² (1-v2 y (1-x2) = f & + 2to² +928² 482 2 to » 426² C 4260² 28o.c » V= e2627 426² 2to²+4%²

3 x loll Now, after potting rn xo c = 3 x 168 m/sec. seco to = 7200 find, We 2noc va reto +4862 X C 2 X 3 X 1011 (3x108 * x 720082 +44(8x10492 c 0,27 earth frame in is G soi is, travelling speed V = 0·2.7 c where speed of light the