A rocket travels in the x -direction at speed 0.70 c with respect to the earth.

Question

A rocket travels in the x-direction at speed 0.70 c 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) = (2.7×1010 m, 240 s).

What is the spacetime coordinate t of the collision in earth's reference frame?

a pre Problem 36.26 Part A What is the spacetime coordinate z of the collision in earth's reference frame? Express your answer with the appropriate units. A rocket travels in the x-direction at speed 0.70c 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 (z, t') = (2 7 1010 m, 240 s) 1.1x1011 m Submit My AnswerS Give Up Correct Part B What is the spacetime coordinate t of the collision in earth's reference frame? Submit My Answers Give Up Incorrect; Try Again; 3 attempts remaining Provide Feedhack

Explanation / Answer

Given,

x' = 2.7 x1010 m

t ' = 240 sec

x = (x' + vt' )

t = (t' + vx'/c2 )

V = 0.70 c

Hence, = 1/ [1-V2 /c2 ] =  1/ [1- (0.72c2) / c2 ] = 1.4

And, x = (1.4)(2.7 x1010 + 0.7 x 3 x 108 x 240) = 1.1 x 1011 m

and, t =  (1.4) ( 240 + 0.7 x 3 x 108 x 2.7 x 1010/(3 x108)2 )   

= (1.4) (240 + 63 )

= 424.2 sec

thus, spacetime coordinate of the collision in earth's reference frame is : (x, t) = (1.1 x1011 , 424.2 )

(Please rate my answer if you find it helpful, good luck...)

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