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Chapter 36: Q. 46 (page 1060)

Two events in the reference frame Soccur 10msapart at the same point in space. The distance between the two events is2400msin the reference frame S'.

a. What is the time interval between the events in reference frame S'′?

b. What is the velocity of S'relative to S?

Short Answer

Expert verified

a. 12.8μsis the time interval between the events in the reference frame S'.

b. 480cis the velocity of S'relative toS.

Step by step solution

01

Part (a) step 1: Given Information 

We need to find the time interval between the events in reference frameS'.

02

Part (a) step 2:Simplify

Consider:

∆x'=2400mt=10×10-6s

Now, finding the time interval between the events in the reference frameS'

∆t2=c∆t2-∆x2=c∆t'2-∆x'2c∆t'2=c×10×10-62+24002c∆t'2=3,02×106+2.42×106c∆t'2=3.02+2.42×106c∆t'2=3.841×103∆t'=3.841×1033×108∆t'=12.8μs

03

Part (b) step 1: Given Information

We need to find the velocity of S'relative to S.

04

Part (b) step 2: Simplify

The velocity of S'relative to S

t'=γt-vxc2→v=0.480c

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