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Chapter 36: Q. 55 (page 1061)

Two rockets, A and B, approach the earth from opposite directions at speed 0.80c. The length of each rocket measured in its rest frame is 100 m. What is the length of rocket A as measured by the crew of rocket B?

Short Answer

Expert verified

The length of rocket A as measured by the crew of rocket B 22 m.

Step by step solution

01

Given information

We have given that, two rockets, A and B, approach the earth from opposite directions at speed 0.80c. The length of each rocket measured in its rest frame is 100 m.

02

Step 1.

Let us assume that, S be the earth’s frame of reference, and S′ be the rocket B's frame of reference. S′ moves with a velocity v = −0.8 c relative to S. In S, rocket A has a speed u = 0.8c.

03

Step 2. 

Using the Lorentz velocity transformation equation to calculate the speed of rocket A as observed from rocket B :

u'=u-v1-uvc2

u'=0.8c-(-0.8c)1-(0.8c)(-0.8c)c2

u'=0.976c

The length of rocket A from rocket B is :

L=(100m)1-(0.976)2

L=22m

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