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Chapter 36: Q. 55 (page 1061)

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

Short Answer

Expert verified

The length of the rocket Aas measured by the crew of rocket Bis 21.95m.

Step by step solution

01

Given Information 

We need to find the length of rocket A as measured by the crew of rocket B.

02

Simplify

Speed of rockets with respect to earth is u=v=0.9c. So the relative speed of the rocket with respect to each other is

vr=u+v1+uvc2=0.8c+0.8c1+0.8c×0.8cc2=0.97c

Here,Lis the length seen from each rocket to other rocket then we have

L=lγ=l1-v2rc2

At last, we know that l=100m. So

L=100×1-0.97c2c2=21.95m

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