A cosmic ray (an electron or nucleus moving ar speeds close to the speed of light) travels across the Milky Way at a speed of 0.98 times the spee of light. If the Milky way is 30,000 pc across, how long does this journey take in our (essentially stationary) frame of reference and the cosmic ray's frame of reference, in years?

Cosmic ray's frame of reference: 99,875 years

Stationary frame of reference: 501,891 years

Explanation:

First of all, we convert the distance from parsec into metres:

The speed of the cosmic ray is

where

is the speed of light. Substituting,

And so, the time taken to complete the journey in the cosmic's ray frame of reference (called proper time) is:

Converting into years,

Instead, the time elapsed in the stationary frame of reference is given by Lorentz transformation:

And substituting v = 0.98c, we find:

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2