Question

A cosmic ray travels $60km$through the earth’s atmosphere in$400ms$, as measured by experimenters on the ground. How long does the journey take according to the cosmic ray?

Short answer

t' = 346.4 micro sec

Step-by-step solution

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

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