An unstable particle is created in the upper atmosphere from a cosmic ray and travels straight down toward the surface of the earth with a speed of 0.99540c relative to the earth. A scientist at rest on the earth's surface measures that the particle is created at an altitude of 45.0km.
(a) As measured by the scientist, how much time does it take the particle to travel the 45.0km to the surface of the earth?
(b) Use the length contraction formula to calculate the distance from where the particle is created to the surface of the earth as measured in the particle's frame.
(c) In the particle's frame, how much time does it take the particle to travel from where it is created to the surface of the earth? Calculate this time both by the time dilation formula and from the distance calculated in part (b). Do the two results agree?