Question

A muon is created 50 km above the surface of the earth. In the earth's frame, the muon is traveling directly downward at 0.9999c.

Part A

In the earth's frame of reference, how much time elapses between the muon's creation and the time it reaches the surface?

Part B

Use time dilation to determine, in the muon's frame, how much time elapses between the muon's creation and the time it reaches the surface.

Part C

In the muon's frame of reference, length contraction reduces the distance between the point at which it is created and the surface of the earth. What is this distance?

Answer 1

A) In earth's frame of reference the muon traveled a distance d=50 km with a speed of v=0.9999 c

Hence, in earth's frame of reference time taken by the muon to reach the surface is

B) However in the muon's frame due to such high speed time dilation has taken place.

So, time elapsed in muon's frame of reference is given by the time dilation formula

t' is the dilated time, v is the velocity of the muon and c is the velocity of light.

Putting the values, time elapsed in muon's frame of reference is

C) Also due to such high speed length contraction took place and the muon traversed a much smaller distance in it's own frame of reference.

Contracted length is given by

l is the contracted length and l_0 is the original length.

Putting the values,