Question

A cosmic ray travels 60.0 km through the earth's atmosphere in 500 μs , as measured by experimenters on the ground. You may want to review

Answer 1

Answer:

t' = 458.26 μs

Explanation:

given,

distance traveled by the cosmic ray = 60 Km

time = 500 μs

time taken for the journey according to cosmic ray = ?

now,

 $v =\dfrac{distance}{time}$

 $v =\dfrac{60\times 10^3}{500\times 10^{-6}}$

      v = 1.2 x 10⁸ m/s

according to time dilation formula

$t' = t\sqrt{1-\dfrac{v^2}{c^2}}$

$t' = 500\sqrt{1-\dfrac{(1.2\times 10^8)^2}{(3\times 10^8)^2}}$

     t' = 500 x 0.9165

    t' = 458.26 μs