Define proper length.

A charged pion decays spontaneously in a time of 26 ns as measured in the frame of reference in which it is stationary. The pion moves with a velocity of 0.96c relative to the Earth. Calculate the pion’s lifetime as measured by an observer on the Earth.

In the pion reference frame, the Earth moves a distance X before the pion decays. In the Earth reference frame, the pion moves a distance Y before the pion decays. Demonstrate, with calculations, how length contraction applies to this situation.

the length of an object in its rest frame

\(\frac{1}{{\sqrt {\left( {1 - {{0.96}^2}} \right)} }}\) OR \(\gamma  = 3.6\)
ECF for wrong \(\gamma\)

93 «ns»
Award [2] for a bald correct answer.

«X is» 7.5 «m» in frame on pion

«Y is» 26.8 «m» in frame on Earth 

identifies proper length as the Earth measurement
OR
identifies Earth distance according to pion as contracted length
OR
a statement explaining that one of the length is shorter than the other one