Two space ships are attempting a docking maneuver and are relaying their coordin
ID: 1471188 • Letter: T
Question
Two space ships are attempting a docking maneuver and are relaying their coordinates to each other as they get closer together. The communication officers of each ship announce the coordinates at the same instant the coordinates are transmitted to the other ship. The ships are 52 km apart. We wish to find whether the ships receive each others' coordinates first, or whether the other shipmates hear their communications officer first, given that the shipmates are within 2.3 meters of their respective communications officers. The speed of sound is 343 m/s. How long does it take for the sound to reach the shipmates?
s
How long does it take for the light to reach one ship from another?
s
Therefore, which happens first?
The ships receive the signal first.Other ship mates hear the sound first.
Explanation / Answer
The time taken by the sound to reach the other shipmates is
t = distance between the officer and other shipmates / velociity of sound
t = 52002.3 m / 343
t = 151.615 s = 2 min 31.615 s
The time taken by the light signals to reach other ship is
tl = distance between the two space ships / velocity of light
tl = 52000 m / 3 x 108 m/s
tl = 1.73 x 10-5 s = 0.0000173 s
Therefore THE LIGHT SIGNALS OF COORDINATES REACH THE SPACE SHIP FIRST THAN SOUND SIGNALS TO THE OTHER SHIPMATES as the time taken by the ligt signals is less than that of the sound signals.
Therefore SHIP RECEIVES THE SIGNALS FIRST THAN SHIPMATES.
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