The figure shows one of four star cruisers that are in a race. As each cruiser p
ID: 2306027 • Letter: T
Question
The figure shows one of four star cruisers that are in a race. As each cruiser passes the starting line, a shuttle craft leaves the cruiser and races toward the finish line. You, judging the race, are stationary relative to the starting and finish lines. The speeds ve of the cruisers relative to you and the speeds vs of the shuttle craft relative to their respective starships are, in that order, (1) 0.70c, 0.40c; (2) 0.40c, 0.70c; (3) 0.20c, 0.90c; (4) 0.50c, o.60c (a) without written calculation, rank the shuttle craft according to their speeds relative to you, greatest first. (b) Still without written calculation, rank the shuttle craft according to the distances their pilots measure from the starting line to the finish line, greatest first, (c) Each starship sends a signal to its shuttle craft at a certain frequency fo as measured on board the starship. Again without written calculation, rank the shuttle craft according to the frequencies they detect, greatest first. Starting line Finish line (a) speed relative to you T2 ? (b) measured distance 4 (c) frequency detected T1 ? 1. 3 24 1 2. 12 34 3, 4 > 1=2>3 4. 14 2> 3 5. 3 12 4Explanation / Answer
a) VS/C = VS/O - VC/M
Where,
VS/C = Velocity of the shuttle wrt cruiser.
VS/O = Velocity of the shuttle wrt the oberver.
VC/O = Velocity of the cruiser wrt the oberver.
Therefore we find that
VS/O = VS/C + VC/O , whi9ch comes out to be 1.1c in all the 4 cases. Hence option 2 is correct.
b) Distance measured by the shuttle craft is directly proportional to the relative speed of the shuttle craft wrt to the cruiser as the slower the cruiser and faster the shuttle craft more will be the distance measured. Hence option 1 is correct
c) Frequency is measured fastest by the shuttle craft that is closest to the cruiser. Hence slower the velocity of the shuttle craft wrt to the cruiser faster is the frequency detected. Hence option 4 is correct.
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