(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Two Rockets A and B depart from Earth at constant speeds of 0.6c in opposite directions, having synchronized clocks with each other and with Earth at departure. After one year as measured in Earth's reference frame, rocket B emits a light signal(call this event E1). At what times, measured in the reference frames of the earth and of rockets A and B, does rocket A receive the signal(event E2)

2. Relevant equations

Lorentz Transformation

kinematics

Time Dilation

signal travels at speed of light

3. The attempt at a solution

So first I just did a simple conversion to get seconds, t_{earth}= 3.15X10^{7}s.

Next, I solved for each of the rocket's respective distances at that point with simple kinematics and obtained (-)5.67X10^{15}m.

After this, I drew myself a coordinate system saying the earth is the origin, rocket B(transmitting signal) in the positive direction, rocket A in the negative direction.

Then I argued that at a time t, the signal and rocket A will be at the same position for the signal to be received and therefore:

position of rocket A = -5.67X10^{15}m- 0.6ct

position of signal = 5.67X10^{15}m - ct

position of rocket A = position of signal

I then solved for t and got 9.45x10^{7}s after the signal is sent. I then added this to the original 1 years time and got 1.26x10^{8}s.

That was for the earth's frame.

For the frame of rocket B and A,

I first took the time dilations for them which should be the same since their speeds are the same just in different directions.

for rocket A/B time = t_{earth}*[tex]\gamma[/tex]

where [tex]\gamma[/tex]= 1/([tex]\sqrt{1-(v^2/c^2)}[/tex]

I got 3.94x10^7s for their dilated year

and for their velocities, I got (-)1.875x10^{8}m/s after applying velocity addition in relativity

with those information, I solved for the distance as observed by rocket a/b and obtained:

1.48x10^{16}m from each other.

Now for observer b, I used the following kinematics:

position of signal = -ct

position of rocket A = -1.48x10^{16}m - 1.875x10^{8}*t

position of signal = position of rocket A

the answer I got when I solved for t was 1.32x10^{8}s from the time the signal was sent.

I added that t to the dilated years time and got 1.71x10^{8}s total for observer rocket B

Lastly, for rocket A I used the same information. The only difference is thekinematics equation:

speed of signal = 1.48x10^{16}- ct

speed of rocket A= 0

solving for t I got 4.93x10^{7}seconds and adding to the dilated year I got

8.87x10^{7}s total.

Please check if my thought process/math is right? Thanks!!!!! :)

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# Homework Help: Relativistic rockets answer check

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