How Do Lorentz Transformations Apply to Aircraft Communication Delays?

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Lorentz transformations are necessary to analyze communication delays between two aircraft landing at different times in New York and San Francisco, separated by a distance of 3,800 km. The key question is whether a signal sent from the first aircraft after touchdown will reach the second aircraft before its own touchdown. Given the time difference of 0.01 seconds, the average speed of the signal must be calculated to determine if it exceeds the speed of light, c. The calculations suggest that the signal's speed is less than c, confirming that the second pilot will not receive the signal before landing. This analysis highlights the implications of relativistic effects on communication in aviation scenarios.
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Ok, I think for this problem you have to use the Lorentz transformations, but I'm not sure how to consider the velocity.

Question:
At 9 hrs 0min 0sec an aircraft touches down in NY. At 9hrs 0min 0.01sec an aircraft touches down in San Francisco. The (straight) distance between the two is 3.8x10^3km.
a) show that any signal that thepilot of the first aircraft sends after the instant of touchdown will reach the second pilot after his own touchdown.

So, for this x=3.8x10^3km, deltat =0.01sec, but if the aircrafts are stationary, what is the velocity? If it is a singnal, is this just c?
 
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Quelsita said:
Ok, I think for this problem you have to use the Lorentz transformations, but I'm not sure how to consider the velocity.

Question:
At 9 hrs 0min 0sec an aircraft touches down in NY. At 9hrs 0min 0.01sec an aircraft touches down in San Francisco. The (straight) distance between the two is 3.8x10^3km.
a) show that any signal that thepilot of the first aircraft sends after the instant of touchdown will reach the second pilot after his own touchdown.

So, for this x=3.8x10^3km, deltat =0.01sec, but if the aircrafts are stationary, what is the velocity? If it is a singnal, is this just c?

Well, this one looks fairly easy...what is the expression for the average speed v_{ave}of any signal that travels a distance {\Delta}x in a time {\Delta}t? If you plug in the distance above along with your {\Delta}t how fast would the signal have to be? Is it greater or less than c?
 

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