This is an IB problem from November 2017. Two rockets are separated by 6E8m (2 sec x c, or two light-seconds), w.r.t. Earth, and are approaching Earth from opposite directions. Rocket A approaches from left at 0.6c. Rocket B approaches form right at 0.4c.(adsbygoogle = window.adsbygoogle || []).push({});

According to Earth, when do they meet? I get 2sec. All seems good.

According to A, how fast is B? Using Lorentz transformation for velocity, I get 0.81c. All seems good.

According to A, how long until A and B meet? So I treat the rockets as if in a train car moving right, with rocket A at the far left of the car (stationary w.r.t. the car) and B moving leftward (at 0.81c w.r.t. the car) from the right end of the car. The car is two light-seconds long, w.r.t. Earth.

I use v=0.6c in gamma to change the time of the event (rockets coming together to meet). I use gamma to transform Earth's perception of an event of 2sec to an event w.r.t. A of 1.6sec.

But if I do this a different way, finding the initial distance between rockets w.r.t. A and then using rate x time = distance (all w.r.t. A), I get 0.81c x time = 2sec x c/gamma (gamma = 5/4, using v=0.6c). Therefore, time=1.98sec.

I tried using the Lorentz transformation for time, to get a tie-breaker, but had no luck. I got t'=gamma(using v=0.6c) (t-vx/c^2) = 5/4 (2sec - 0.6c (2 sec c)/c^2) = 1sec.

Thanks for any help in pointing out where I'm making my mistakes.

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# Rockets approach: time they meet w.r.t. rocket A?

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