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Chapter 36: Q. 26 (page 1060)

A rocket travels in the x-direction at speed 0.60c 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')=(3.0×1010m,200s). What are the spacetime coordinates of the collision in earth’s reference frame?

Short Answer

Expert verified

γ=1.25x=8.25×1010mt=325s

Step by step solution

01

Given Information

We have given that a rocket travels in the x-direction at speed 0.60cwith respect to the earth.

The collision's spacetime coordinates are(x',t')=(3.0×1010m,200s).

We have to find the spacetime coordinates of the collision in earth’s reference frame.

02

Simplify

We have,

γ=1-vc2-1/2γ=1-(0.6)2-1/2γ=1.25

Lorentz transformation in Earth's frame yields:

x=γ(x'+vt')=1.23×1010m+(0.6)(3×108m/s)(200)=8.25×1010mt=γt'+vx'c2=1.25200+(0.6)(3×108m/s)(3×1010m)(3×108m/s)2=325s

Therefore,

γ=1.25x=8.25×1010mt=325s

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