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Chapter 37: Q. 13 (page 1082)

A cosmic ray travels 60kmthrough the earth’s atmosphere in400ms, as measured by experimenters on the ground. How long does the journey take according to the cosmic ray?

Short Answer

Expert verified

t' = 346.4 micro sec

Step by step solution

01

Step 1. Given:              d = 60 km = 60000 m ;             t = 400 * 10 ^ - 6 s

We Know ;

v = d/t = 60000 / ( 400 * 10 ^ -6 ) = 1.5 * 10 ^ 8 m/s

02

Step 2. How long does the journey take according to the cosmic ray ?

t' = t * sqrt [ 1 - ( v / c) 2 ]

t' = 400 * 10 ^ 6 * sqrt ( 1 - ( (1.5 * 10 ^ 8 / (3 * 10 ^8) ) ^ 2 )) = 346.4 * 10 ^ -6s = 346.4 micro sec

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