SIN练习题第1题答案解析

SIN练习题1

1.Romeo sets off in his spaceship to marry Juliet, who lives on the planet Lovelon, 10 light-years away from earth. He can accelerate at 15 m/s2, and must decelerate at the same rate, in order to stop at Lovelon. Unknown to him, Juliet has taken an earlier shuttle back to Earth and she will wait there. Since there is no communication, Romeo will have to travel back again! Romeo left yesterday, on April 30, 1997. What is the earliest year in which they can be wed? Romeo and Juliet are both classical persons, and they ignore any relativistic effects! 1 light-year is about 9.46 x 1015 m.

(A) 1999 (B) 2004 (C) 2007 (D) 2047 (E) THEY WILL DIE FROM OLD AGE FIRST

SIN练习题1答案及解析

（答案：C）解析：

This is a straightforward s = (1/2)a t2 problem, to ease students into the exam. It's easy to calculate the time to get to Lovelon, and each light year represents 1 light-year = 365 days/year x 24 hours/day x 3600 seconds/hour x 3 x 108 m/s = 9.46 x 1015 m.If Romeo travels all the way there at 15 m/s2, then 10 light-years will take him a time given by 10 x 9.46 x 1015 = 1/2 x 15 (time)2 giving 1.123 x 108 seconds, or 3.56 years, and he will be moving at 16.85 x 108 m/s, which in Startrek language is Warp 5.6! This won't do him much good of course, because he will pass Lovelon at this speed. Romeo has to travel half-way to Lovelon, 5 light-years, then reverse his rockets to decelerate for another 5 light years at 15 m/s2, so that he arrives at low speed for docking. This splits the journey exactly in half, due to the obvious symmetry of the motion. At the half-way point he'll be moving at 11.9 x 108 m/s, which is near enough Warp 4!

It'll take him 7.94 x 107 sec to get half-way, about 2.51 years, so the total time to get to Lovelon and then back to earth will be 4 times this, or 10.07 years. They can wed in 2007 (C).

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