Answer:
Q1) Time taking by particle to travel the 40 km wrt. earth = sec.
Q2) The distance traveled by particle where the particle created to surface of earth wrt. particle's frame = 3.84 km.
Q3) The time taking by particle to travel from where it is created to the surface of the earth = sec.
Explanation:
Given :
Speed of particle wrt. earth
Distance between where particle is created and earth surface = 40 km
we know that,
⇒
Where , , we know speed of light
∴
∴ Thus, time taking by particle to travel the 40 km wrt. earth
According to the lorentz transformation,
⇒
Where improper length, proper length (distance measured wrt. rest frame) = 40 km
km
∴ Thus, the distance traveled by particle where the particle created to surface of earth wrt. particle's frame = 3.84 km.
According to the time dilation,
Where improper time (wrt. earth frame time) , proper time (wrt. particle frame).
Thus, the time taking by particle to travel from where it is created to the surface of the earth .