I tried doing this problem. I got 470ms. How is the answer 440ms? Shouldn\'t the
ID: 2020100 • Letter: I
Question
I tried doing this problem. I got 470ms. How is the answer 440ms? Shouldn't the time by the observers be larger?
Two fixed navigation beacons mark the approach lane to a star. The beacons are in line with the star and are 40 x 106 m apart. A spaceship approaches the star with a relative velocity of 0.30 c and passes the beacons. The passage of the ship between the beacons is timed by observers on the beacons. The time interval of the passage according to observers is closest to:
A. 470 ms
B. 420 ms
C. 250 ms
D. 440 ms
E. 170 ms
Explanation / Answer
The given distance between the star and the beacons=s=40*10^6 m
Velocity of the given spaceship=0.30 c
The passage of the ship between the beacons is timed by observers on the beacons
t=t0 /(1 - v2/c2)
=(s/v)/(1 - v2/c2)=(40*10^6 m/0.30c)(1 - 0.302)
=0.44/0.954=0.465 seconds=465 ms
So, the options are not correct.