A rocket travels in the x-direction at speed 0.7 with respect to the earth. An e

Question

A rocket travels in the x-direction at speed 0.7 with respect to the earth. An experimenter on the rocket observes a collision between two comets and determines that the spacetime coordinates of the collision are (x',t') = (2.7x10^10,160).

What is the spacetime coordinate of the collision in earth's reference frame?
Express your answer using two significant figures.

So I'm not sure if I've calculated it wrong, I tried a few times, and got 1.44×10^4, -2.94×10^10, and -9.24×10^9. They were all wrong. There's another part to the question asking for the time in the reference frame, but once I find out what I did wrong here, I can work it out myself.

Explanation / Answer

space & time co-ordinates : (Inverse trans -formation) (Inverse trans -formation) x = (x' + vt' ) t = (t' + vx'/c2 ) given: x' = 2.7 x1010 m t ' = 160 sec find : (x,t ) where V = 0.7 c thus, = 1/ [1-V2 /c2 ]                =  1/ [1-0.72c2 /c2 ]                = 1.4 thus, x = (1.4)(2.7 x1010 + 0.7 x3x108 x 160)              = 8.484 x1010 m   and   t =  (1.4) ( 160 + 0.7 x3x108 x 2.7x1010/(3 x108)2 )                 = (1.4) (160 +0.63 )              = 224.882 sec thus, spacetime coordinate of the collision in earth's reference frame is : (x, t) = (8.484 x1010   , 224.882 )

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